raattgift

Maybe you want to leaf through a copy of Birrell & Davies or Parker & Toms again. QFTCS is good in strong gravity, and is as good as anything else at transplanckian scale (which is to say there's presently no way of knowing when around there QFTCS becomes a bad approximation to an unknown quantum gravity).

We should also remember the enormous cosmological curvature in which testable quantum systems exist; it's not just about compact objects. Significant? There's observed H-sources above z ~ 15, and of course the CMB photons at z ~ 1100. Indeed, B&D deals with Robertson-Walker spacetimes over several chapters before they get to black holes.

Also at the weak but measurable curvature regime there's e.g. Pound-Rebka, time metrology[1], and so forth, and lots of spacecraft confirming the strong equivalence principle (e.g. MESSENGER, LAGEOS) and thus supporting the LLI one expects to find in relativistic QFTs of the sort one would use to describe the behaviour of laser altimeters, distant astrophysical masers (and the Lyman-alpha forest), the spectral lines in stellar atmospheres and so on.

[1] just because it's neat and directly relevant to your comment: https://journals.aps.org/prxquantum/abstract/10.1103/q188-b1... [2025]

In a terminal window run

  log stream --predicate 'subsystem == "com.apple.TimeMachine" AND NOT (category == "LogLimits" OR category == "VolumeViewModel")' --info --debug --style compact

  man log

  man tmutil

Some things to look out for are what filesystem your newly formatted external volume is (APFS might not be great for a single spinny disk, for example), and what version of USB is in use (friends don't let friends do USB 2 mass storage). With inexpensive external media it's often a cable or power supply issue, even if (as in your case) tar appears to work. Have you checked that the contents of the tar file are correct? Also, tar files tend to be streamed out to sequential LBAs, where smaller files and (in Time Machine backups) holes might lead to a different write pattern that the drive might not like. Maybe test with rsync -c instead of tar?

Indy led Belloq to the Ark. Belloq was looking in the wrong place because he only had the side of the headpiece of the Staff of Ra that was seared into Toht's palm, thus without Jones in the movie, the Nazis might never have acquired the Ark, failing to "take back one kadam to honor the Hebrew God, whose Ark this is".

Moreover, if Indy had not gone to Nepal, then Toht (having obtained the headpiece) and Belloq might have used a staff of the right length to find the Ark. Had they also captured Marion and taken her along to their secret island base, Jones would not have been there to tell her not to look, and thus her face would have melted off too.

Of course, Toht and his henchmen might also just have killed her in Nepal.

Alternatively, as Toht and company followed Jones to Marion, and might not have found her otherwise, they might never have had even half the headpiece of the staff of Ra, and the Ark thus would have remained undisturbed in its resting place, leaving the baddies to deal merely with the wrinkles and creases associated with aging appearing on their faces in the fullness of time.

So: Jones keeps Ravenwood alive, and puts the Belloq and his Nazi colleagues in a position to have their faces melted off. Jones also offed a couple of Nazis and other baddies along the way.

Cool, so the European Union and overlapping institutions could see this as an opportunity to promote greater public knowledge about one of their respective member states. Seems like an argument in favour of encouraging the display of a member state's flag rather than that of a non-member-state or former member state (especially given that state's history with respect to Ireland).

Using flags alone is already poor UI since there are many languages which spill across the borders into multiple member states and non-member states, and some member states with multiple official and commonly spoken languages.

But a menu item that reads: [Irish flag] (English) like one that reads [Swedish flag] (Svenska) does not seem worse than the legacy use of the UK flag or the popular use of the US one.

That said, whenever there is a language selection UI (e.g. at banking machines or institutional websites) in wider Europe that uses flags to represent languages -- probably not a good idea to start with, but very common -- the Irish tricolour should be used to indicate English rather than the UK or USA flags. (although cf Airteagal 8 of Bunreacht na hÉireann).

Several of her first-or-sole-author minimal length quantum gravity phenomenology papers have more than a hundred citations:

https://scholar.google.com/citations?user=NaQZcyYAAAAJ&hl=en

and if nothing else, that's strong evidence that she has made a contribution to academic dialogue in that area.

Hossenfelder et al. 2003 in particular, is quite striking for an early career researcher: <https://scholar.google.com/citations?view_op=view_citation&h...>. Also noteworthy are several early publications on either side of her 2003 doctoral thesis on microscopic black holes in large extra dimensions. In that period numerous co-authors, reviewers, and editors supplied indirect evidence against your claim that her papers "were pretty bad".

Quite a lot of strong constraints on large extra dimensions came out of the LHC work eight to twelve years after these publications. Her old link-rotting written blog captures some of that: <https://backreaction.blogspot.com/2011/06/extra-dimensions-a...>, for instance.

There is an enormous difference between being wrong and publishing nonsense.

at least those I read

You could have usefully supplied a short annotated bibliography. It would certainly make your final sentence

She is pure show

less likely to be seen as nonsense and more likely to be seen as wrong.

Whatever she has become in the past couple of years, she was certainly not pure show in the first eight or so years after her doctorate.

No, not really. To boil it down to thinner text, and to focus on your "Space becomes timelike", I think you are stuck on (a) a particular system of coordinates that (b) are not regular across the horizon and (c) thinking that either of these does anything physical to free-falling infalling test particle.

The huge flashing red warning sign on (a) & (c) is that you drop in the words "'upward' direction", "{toward, closer to, away from} the singularity" and most especially "slower": you are clearly implicitly slicing spacetime into space and time.

If you can handle thicker text, Unruh has a nice discussion of regular systems of coordinates at http://theory.physics.ubc.ca/530-21/bh-coords2.pdf Additionally, Martel & Poisson 2001 <https://pubs.aip.org/aapt/ajp/article-abstract/69/4/476/1055...> (arXiv version <https://arxiv.org/abs/gr-qc/0001069>) is a nice discussion of PG coordinates.

More visually, one can compare the light cone structure on a KS diagram like at <https://tikz.net/relativity_kruskal_diagram/> (just before the "Edit and compile if you like") and a randomly chosen but very typical diagram in Schwarzschild coordinates <https://www.researchgate.net/profile/Ward-Vleeshouwers/publi...> or (in German) <https://yukterez.net/f/einstein.equations/files/schwarzschil...> (hovering over a diagram displays some light cones). Which cone appears to topple over in their respective coordinate charts is pretty obvious, and should give you plenty of shaded grey to think about the coordinate-dependence of "Space becomes timelike".

Space becomes timelike. There is only forward ...

No. It's a fanciful analogy on a particular family of coordinate charts, particuarly systems of coordinates which do not smoothly/regularly cross the horizon. The black hole interior is still part of a Lorentzian manifold, there is no change of the SO+(1,3) proper orthochronous Lorentz group symmetry at every point (other than spacetime points on the singularity). One can certainly draw worldlines on a variety of coordinate charts and add light-cones to them, and observe that the cones interior to the horizon all have their null surfaces intercept the singularity. However, there's lots of volume inside the interior light cones (and on the null surfaces) and nothing really constrains an arbitrary infaller's worldline, especially a timelike infaller, to a Schwarzschild-chart radial line (just as nothing requires arbitrary infallers to be confined to geodesic motion).

The interior segment of a Schwarzschild worldline in general can't backtrack in the r direction, but there are of course an infinity of elliptical trajectories which don't. (That is to say that all orbits across the horizon are plunging orbits; but one can also say that of large families of orbits that cross ISCO, which is outside the horizon).

A black hole with horizon angular momentum and general charges offer up different possibilities, as does the presence of any matter near (including interior to) the horizon (all of these also split the ISCO radius, move the apparent horizon, and may split the apparent and event horizons). The Schwarzschild solution of course is a non-spinning, chargeless, vacuum solution everywhere, and is maximally symmetrical, and is usually probed with a test particle. An astrophysical system like a magnetic black hole formed that passes through a jet from a companion pulsar, for example, does not neatly admit the Schwarzschild chart (and has no known exact analytical solution to the field equations). At least one such astrophysical binary is known (in NGC 1851 from TRAPUM/MeerKAT) (and if you don't immediately run away from A. Loeb papers like you should, he added his name to one that argues there are thousands of such systems in the galaxy centre near Sgr A*, which itself is now known to have strong magnetic fields (thanks to EHT's study of the polarized ring)).

The relevant quantities are the curvature scalars near the horizon, and for a sizable black hole they are small there. As an example, consider the Kretschmann scalar (KS). The KS is the sum of the squares of all components of a tensor. In Schwarzschild spacetime KS looks like R_{\mu\nu\lambda\rho}R^{\mu\nu\lambda\rho} = (48 G^2M^2)/(c^4r^6), where R is the Riemann curvature tensor, and we can safely set G=1 and c=1 so (48 M^2)/r^6. In this setting, KS is proportional to the spacetime curvature. At r = 2M, the Schwarzschild radius, the number becomes very small as we increase M, the black hole's mass. However, for any M at r = 0, the Kretschmann scalar diverges.

For a large-M black hole, there is "no drama" for a free-faller crossing the event horizon, as the KS gradient is tiny.

Since the crosser is in "no drama" free-fall he can raise his hands, toss a ball between his hands, throw things upwards above his head, and so forth. The important thing though is that all these motions are most easily thought of in his own local self-centred freely-falling frame of reference, and not against the global Schwarzschild coordinates. His local frame of coordinates is inexorably falling inwards. Objects moving outwards in his local frame are still moving inwards against the Schwarzschild coordinates.

You might compare with a non-freely-falling frame of reference. Your local East-North-Up (ENU) coordinates let you throw things upwards or eastwards, but in less-local coordinates your ENU frame of reference is on a spinning planet in free-fall through the solar system (and the solar system is in free-fall through the Milky Way, and the galaxy is in free-fall through the local group). That your local ENU is not a freely-falling set of coordinates does not change that the planet is in free-fall, and your local patch of coordinates is along for the ride.

A comparison here would be a long-running rocket engine imparting a ~ 10 m s^-1 acceleration to a plate you stand on. In space far from the black hole, you and the rocket engine would tend to move away from the black hole, but you'd be able to do things like juggle or jump up and down, and it'd feel like doing it on Earth's surface. This is a manifestation of the equivalence principle. Inside the horizon the rocket would still be accelerating the plate and you at ~ 10 m s^-1, but you, the plate, and the rocket would all be falling inwards.

The "river model" you mean isn't very general, as one eventually becomes interested gravitating systems where there isn't a suitable congruence, e.g. in close binary compact objects. In such systems, one has to add terms analogous to turbulence, frustrating calculability (and the development of relativistic intuition). It also doesn't deal well with tides: for example, Schwarzschild infaller worldlines (even on a body like the moon, where there is no horizon) on widely separated radial trajectories converge in a way that is unlike the confluences of rivers and their tributaries. These models really only assist in understanding a single (spatial) radial line with possibly multiple successive "rafts" of matter bound to it (at different times), and in a set of PG-like coordinates useful for a particular distant observer. From there one symmetrizes: all observers and all radial lines are identical (speherical symmetry) and successive "rafts" all take the same radial line (static spacetime). Without this symmetrization, a black hole is an infinite number of slightly different rivers, and then you might as well solve the equations of motion in the standard way.

For understanding a handful of highly symmetrical systems, it might help a student understand some intuitions about what Killing vector fields and congruences (notably those made by choosing the velocity vector field of a set of geodesics) are, and tends to lead into an investigation of what the shift vector in a 3+1 decomposition represents.

For calculating things like the spherical orbits around or the photon surface of a real black hole like our galaxy's central Sgr A*, the river model seems outright unhelpful. For example, how does a river model help to understand https://duetosymmetry.com/tool/kerr-circular-photon-orbits/ ?

time moving at a constant rate

This is another way of saying slicing of a Lorentzian (4d) spacetime into non-overlapping spaces organized along an arbitrarily chosen future-directed non-spacelike worldline. That is, this is a 3+1 slicing. We can slice along your worldline, or on that of a neutral hydrogen atom floating in intergalactic space, or on that of a high-energy cosmic ray, or on that of a CMB photon. It's arbitrary, and each can give markedly different spatial slices through the same spacetime (in particular particle counts on slices will differ where the choices of index axes are anywhere accelerated with respect to one another).

When we decompose in this way, and take an <https://en.wikipedia.org/wiki/ADM_formalism> approach, we will tend to think of the shift vector as how we associate a point one one slice (everywhere in space at a coordinate instant in the spacetime) with its successor slice (everywhere in space at the next coordinate instant int he spacetime), which is helpful when spacetimes expand or contract in one or more spatial directions along the arbitrarily chosen time axis.

Braeck & Gron 2012 have a good bit of pedagogy about the river analogy and a fine set of references <https://arxiv.org/abs/1204.0419> and of course point to Hamilton & Lisle 2008, as originators of the analogy <https://arxiv.org/abs/gr-qc/0411060>.

See also the more technical https://astrobites.org/2025/07/02/unburnt-helium-sne-ia/

If everything must be constrained to the lattice points, yes. However, empty space has high Boltzmann entropy: you can cut a patch of empty space from here and swap it for the same volume of empty space from there, and the two coarse grain macrostates will be indistinguishable.

Expanding de Sitter quasi-vacuum has tremendous growth in entropy. Gibbons and Hawking gives this (for 3+1d de Sitter) as a quarter of the horizon area: S_H = \frac{Area_{H}}{4} \sim H^{-2} with the "quasi-" giving us increasing growth in the horizon area as DoFs exit the horizon compared to classical pure de Sitter vacuum.

I'm not sure how confining some species of matter to expanding lattice is different from quasi-vacuum in the limit where the lattice spacing is large. I guess you have to abolish continuum spacetime in favour of a taxicab geometry with an analogue of dark energy? Otherwise, how does it differ from an isotropic homogeneous FLRW dust?

The (Newtonian) Shell Theorem is fairly sensitive to spherical symmetry. In General Relativity one can write down a metric wherein inside any boundary surface there is flat spacetime. It's easiest to do this for a spherical boundary, but one can work out a metric which is axisymmetric (e.g. oblate and spinning or prolate and tidally deformed) and probably all sorts of other weird shapes following ideas from Gauss's Law for Gravitation. Writing down a metric for that is hard though -- really hard if the idea is to make it time-independent, and really really hard if the idea is to make it time-dependent but static (as in a complex Gaussian surface doesn't relax into a more spherical shell). For example, bumps raised on each other by binary black holes will vanish after merger (or if they fly away on hyperbolic trajectories, having "grazed" each other), leaving you with a spherical horizon (if nonspinnning) or an oblate one (if spinning).

Essentially to break spherical symmetry (or axisymmetry where there's spin) and keep it broken you have to introduce something like a dark energy. One can do that outside (retaining flat space inside) or inside (leading to the equivalent direction-dependent attraction of outside objects).

The local theory part of the Carney et al paper (preprint <https://arxiv.org/abs/2502.17575>) is interesting in that it isn't obviously related to string theory / holographic entropic gravity. Instead masses induce a spin polarization near them which is a lower entropy state. Two masses with two polarized spin-clouds will attract each other as the system tries to thermalize to a higher-entropy state. With careful choices of parameters, they can generate any central force, and they explore a particular choice which corresponds to Newtons 1/r^2 mutual attraction.

The paper cannot deal with fast-moving masses at all: it's not just the relativstic regime (where speeds are significant fractions of c) but rather the masses must move more slowly than the thermalization. This is hugely restrictive.

Finally, comparing themselves to the traditional approach of quantizing perturbations (e.g. turning classical (General Relativity) gravitational waves into lots of spin-2 gravitons) the authors write:

  The gravitational interactions we observe at accessible
  length scales could in principle emerge in many ways from
  physics at the Planck scale ρ ∼ mPl/ℓ3 Pl ∼ 10104 J/cm3.
  Perhaps the simplest is that gravitational perturbations
  are quantized as gravitons, i.e., as another quantum field
  theory like the gauge bosons of the other fundamental
  forces in nature. This is a perfectly good effective quan-
  tum field theory; nothing in principle forces us to aban-
  don this picture until energies near the Planck scale.

  we find that the models have a range of free parameters,
  and in some parameter regimes become indistinguishable
  from standard virtual graviton exchange

So while the idea is kinda interesting, I think they are putting the cart before the horse in asking what their model says about things like the interaction between gravitation and entanglement. That's simply unmeasurable by experiment right now whereas the very-well-understood relativistic precession of Mercury's perihelion is completely out of scope for this initial paper.

The bit of math is the Shell Theorem <https://en.wikipedia.org/wiki/Shell_theorem>.

No, here "entropic" is as in the entropic force that returns a stretched rubber band to its unstretched condition, which (as it tends to be scrunched a bit) is at a higher entropy.

https://en.wikipedia.org/wiki/Rubber_band_experiment

"The stretching of the rubber band is an isobaric expansion (A → B) that increases the energy but reduces the entropy"

[apologies for any reversed signs below, I think I caught them all]

In Verlinde' entropic gravity, there is a gravitational interaction that "unstretches" the connection between a pair of masses. When they are closer together they are at higher entropy than when they are further apart. There is a sort of tension that drags separated objects together. In Carney et al's approach there is a "pressure mediated by a microscopic system which is driven towards extremization of its free energy", which means that when objects are far apart there is a lower entropy condition than when they are closer together, and this entropy arises from a gas with a pressure which is lower when objects are closer together than when objects are further apart. Pressure is just the inverse of tension, so at a high enough level, in both entropic gravity theories, you just have a universal law -- comparable to Newton's -- where objects are driven (whether "pulled" or "pushed") together by an entropic force.

This entropic force is not fundamental - it arises from the statistical behaviour of quantum (or otherwise microscopic) degrees of freedom in a holographic setting (i.e., with more dimensions than 3+1). It's a very string-theory idea.

The approach is very hard to make it work unless the entropic force is strictly radial, and so it's hard to see how General Relativity (in the regime where it has been very well tested) can emerge.

Any infalling object at Kruskal diagram crosses the line clearly labeled as t=infinity

Do check out Lemaître and Gullstrand-Painlevé coordinates for the Schwarzschild black hole.

Sorry, I don't want to get into metaphysics.

Black hole mergers are studied using post-Newtonian methods and numerical methods because there is no general analytical approach known. SXS, Simulating eXtreme Spacetimes, and the black hole perturbation toolkit both have web presences, you could start there. There is also an academic literature on matching the waveforms in both regimes. These are checked against results from multimessenger astronomy.

I'd really love to see what shape two Schwarzschild blackholes (and by that I mean their event horizons because, I don't believe anything beyond them is real to us) hitting each other could look like

This is well into the numerical relativity regime.

ETA: I'd pick <https://www.youtube.com/watch?v=jkpfXByQHxA> (SXS collab, "Event horizon for equal mass inspiral BBH in two coordinate systems") and the zoom-in at <https://www.youtube.com/watch?v=p4MTsCDtHMM> from a quickie cruise through some visualizations. There are links in the video description. Do beware that there are several types of horizon involved here, and they will not match your intuitions from Schwarzschild (see the point made in the zoom-in video description) which I would wager are built on the presence of a static Killing field which becomes null at the horizon, but the entire Killing field doesn't exist in these BH merger spacetimes. Roughly, though, if anything is in an orange region, it stays in an orange region. That includes a lot of gravitational radiation moving inwards in the purple region. [ETA again: the related Phys. Rev. D paper <https://arxiv.org/abs/1606.00436> has some nice details about the "duck bill" topology, too, and offers further detail on the purple region.]

https://www.youtube.com/@mpi_grav has several videos particularly in their NR playlist <https://www.youtube.com/watch?v=acHmN2MlJQQ&list=PLSYkic-Csf...>. Look for distortions in the BH horizons (whether it's an apparent horizon or some comparable surface gets into metaphysics; apparent horizons are at least locally observable), particularly the so-called "duck bill". Bear in mind the these are data visualizations principally of the waveforms, and the choices in intensities and hues are probably not going to be aligned with your intuition.

SXS has several videos too https://www.youtube.com/@SXSCollaboration - last month there was a major catalogue reorganization by the SXS collab so it may be that some internal links and semi-recent videos have issues.

And see for example https://www.black-holes.org/2024/10/02/BBH-mergers-with-spec...

Generally such simulations allow one to trace lightlike geodesics as a local probe of the lightlike horizon surfaces.

I don't know which is the case

Exactly. That honest self-admission must be made near the start of any research programme.

tl;dr The farrrr-from-the-horizon part of Schwarzschild spacetime is just not like our spacetime. Only near and outside the horizon (or better, in the absence of a horizon) does Schwarzschild become a decent physical approximation for anything in our universe.

Schwarzschild infinity is unphysical, while your notion of t(Earth) is physical because we can associate a worldline with the planet's centre of mass (COM), hold the COM at the spatial origin of a system of spacetime coordinates, and use whatever "timestamps" we like on the time axis. But we could decide that t(Earth)=infinity could be yesterday, or tomorrow, or a billion years ago, or a couple billion years from now; if we count of seconds before or after t(Earth)=infinity, we still have t'(Earth)=infinity, so it's not a very good choice of coordinate.

I think you have a misunderstanding that is probably beyond my ability to help you with, since we can't do interactive blackboard work in HN comments. The root of your problem seems to be mis-identifying the local time at Earth with the Schwarzschild time at infinity in the Schwarzschild solution. We aren't at infinity to any known black hole: between us and the most distant black holes we know of is expanding spacetime not found in Schwarzschild's solution; betwee us and the nearest black holes is substantially and lumpily curved spacetime and plenty of matter unlike Schwarzschild's unique pointlike mass surrounded by non-lumpy matterless vacuum; none of the astrophysical black holes are infinitely old today (whereas Schwarzchild black holes are infinitely old at every time, otherwise the spacetime would not be static); and in general exact solutions of the Einstein Field Equations -- even ones that are not eternal -- do not superpose cleanly with solutions for other black holes (and crucially there are no black hole mergers in Schwarzschild), ordinary stars, galaxies, clusters, and expanding spacetime. As an example: hover just above the apparent horizon of Sagittarius A*. Look at a stellar black hole in our galaxy. What do you make of infallers plunging towards the smaller black hole? What do you make of the evolution of mass of the stellar black hole, from your vantage point hugging an SMBH's horizon?

Short of taking a series of courses or finding an informal short-term tutor to walk you through particular things (you can find either at your local tertiary education school, like a community college or university), there are plenty of good textbooks on General Relativity. You seem to have found Wald's, which is probably the most rigorously and densely mathematical of several popular teaching choices, and it does not seem to have helped you. I'd guess you'd be better off with e.g. Carroll's Spacetime and Geometry or Wheeler's Gravity and Spacetime.

There is also the Israel-Darmois thin shell method, which is technically annoying but lets us cut the central part of an e.g. Schwarzschild solution and paste it into a cosmology populated with other such pasted-in subregions. We can then trace light rays from e.g. a quasar, across early expanding space to a SMBH or elliptical galaxy acting as a gravitational lens, and then across later expanding space to an approximation of our neighbourhood, adapting the rays at each shell boundary. Although there is very definitely a subregion of black hole solution in that kind of approach, the asymptotically flat part of Schwarzschild is cut away along with its distant infinities. One can compare this cutting and pasting to the Hill sphere of influence of Jupiter and those of its satellites, for example, if one were interested in a navigational plan like Juno's or JUICE's.

In 1+1 dimensions one can analyse the gravitational behaviour of an infinite line of ...-wire-resistor-wire-resistor-... with an adaptation of Bell's spaceship. Throwing away two dimensions eliminates shear and rotation (and all sorts of interesting matter-matter interactions) so we can take a Raychaudhuri approach.

We impose initial conditions so that there is a congruence of motion of the connected resistors, so that we have a flavour of Born rigidity. Unlike in the special-relativistic Bell's spaceship model (in which the inertial motion of each spaceship identical save for a spatial translation), in our general-relativistic approach none of the line-of-connected-reistors elements' worldlines is inertial, and each worldline's proper acceleration points in a different direction but with the same magnitude. This gives us enough symmetry to grind out an expansion scalar similar to Raychaudhuri's, Θ = ∂_a v^a (<https://en.wikipedia.org/wiki/Raychaudhuri_equation#Mathemat...>). As an aid to understanding, we can rewrite this as 1/v \frac{d v}{d \tau}, and again in terms of a Hubble-like constant, 3H_0.

We can then understand Θ as a dark energy, and with Θ > 0 the infinitely connected line of ...-wire-resistor-wire-resistor-... is forced to expand and will eventually fragment. If Θ < 0, the line will collapse gravitationally.

no nucleation sites

If Θ = 0 initially, we have a Jeans instability problem to solve. Any small perturbation will either break the infinite ...wire-resistor-wire-..., leading to an evolution comparable to Bell's spaceship: the fragments will grow more and more separated; or it will drive the gravitational collapse of the line. The only way around this is through excruciatingly finely balanced initial conditions that capture all the matter-matter interactions that give rise to fluctuations in density or internal pressure. It is those fluctuations which break the initial worldline congruence.

This is essentially the part of cosmology Einstein struggled with when trying to preserve a static universe.

In higher dimensions (2+1d, 3+1d) the evolution of rotation and shear (instead of just pressure and density) becomes important (indeed, we need an expansion tensor and take its trace, rather than use the expansion scalar above). A different sort of fragmentation becomes available, where some parts of an infinite plane or infinite volume of connected resistors can undergo an Oppenheimer-Snyder type of collapse (probably igniting nuclear fusion, so getting metal-rich stars in the process) and other parts separate; the Lemaître-Tolman-Bondi metric becomes interesting, although the formation of very heavy binaries early on probably mitigates against a Swiss-cheese cosmological model: too much gravitational radiation. The issue is that the chemistry is very different from the neutral-hydrogen domination at recombination during the formation of our own cosmic microwave background, but grossly a cosmos full of luminous filaments of quasi-galaxies and dim voids is a plausible outcome. (It'd be a fun cosmology to try to simulate numerically -- I guess it'd be bound to end up being highly multidisciplinary).

Not sure what you mean; you can't have any mass in a flat spacetime and obey the Einstein Field Equations for a Lorentzian spacetime (because T_{\mu\nu} doesn't vanish everywhere).

There are a variety of types of variable speed of light. If we foliate to 3+1 the usual picture is that c is constant on all spatial slices. Some VSL theories have the same c at all points on a given slice, but introduce a time variation of c. Other VSL theories introduce spatial variation as well (or instead). These families of theories all have significantly different equations of motion or actions from one another (cf. <https://en.wikipedia.org/wiki/Einstein%E2%80%93Hilbert_actio...>). There's no obvious reason why c couldn't relate in a more complicated way to the stress-energy tensor than the Einstein gravitational constant does, but there's also no obvious reason to think such an alternative theory should produce free-fall trajectories similar to those from GR.

In any case, I think you have to choose your function on c, obtain the field equations, decide which energy conditions and constraint equations you want to impose, set appropriate boundary conditions, choose a curve along which to foliate, and run with enough different initial-value surfaces (each of which must satisfy the constraints initially), that eventually an intuition develops. A Will-like parameterized post-Newtonian formalism approach would also be a good idea (<https://en.wikipedia.org/wiki/Parameterized_post-Newtonian_f...>).

Unfortunately I'm unable to guess your choice of "c(m) formula".

The problem is probably connecting an image of a tilted causal cone at p near but outside a regularized r_s in Schwarzschild spacetime with the idea that from p there is a limited number of null geodesics escaping to the asymptotically flat region, that the fraction decreases with decreasing regularized r coordinate, and that from p' at the trapping surface there are no such null geodesics, as all non-spacelike curves (accelerated or not) at any point on or interior to the trapping surface terminate at the singularity. The idea that the singularity inevitably lies in the future of any observer at p' is behind the "spacetime swap" notion.

Some of the problem is that Schwarzschild coordinates have surprises buried in them, and what \Delta r and \Delta t mean are not what most people tend to think.

Someone should do an ELI12 of Unruh's (ca. 2014) excellent (give or take varying the spelling of Martin Kruskal's surname) Schwarzschild BH global coordinates pedagogic review <http://theory.physics.ubc.ca/530-21/bh-coords2.pdf> and add in a bit on Fermi normal coordinates as a maybe-obvious not-a-chart follow-on to the commenary just above eqn (55). But on "maybe-obvious", Unruh has the choice line: "Since in a large number of cases, the single horizon coordinates were discovered long before Schild’s coordinates, this is an exercise in alternate reality – what could have so easily happened if only the generators of those coordinate systems had recognized what they had."

I think given time at a blackboard we could walk through Newton's cannon in the context of Poisson gravity, and for extra credit with the cannonball inducing a perturbation of the Poisson vector field. Even without the cannonball's backreaction, the Poisson picture offers a nice image of the gravitational potential energy at the top of the cannonball's inertial (ballistic) curve. We would then consider a cosmology like our own but with a recollapse: at maximum extent there is some (quasi-)Newtonian notion of gravitational potential energy for all the galaxies, since they are at the point where they begin free-falling back into a denser configuration. It's then the usual story of relating kinetic and potential energy, and recognizing that the standard cosmological frame is close to Newtonian by design. (We also have to stop this approach when the galaxies are merging enough that radiation pressure and gas ram pressure become relevant, because the errors become astronomical).

Since we don't have a blackboard in front of us to interact with, I can suggest Alan Guth's lecture notes on Newtonian cosmology. (Guth is credited with discovering cosmic inflation.) https://web.mit.edu/8.286/www/lecn18/ln03-euf18.pdf See around eqn (3.3). You could also borrow a copy of Baumann's textbook <https://www.cambridge.org/highereducation/books/cosmology/53...> which studies the Poisson equation for various spacetimes, however a static spacetime gets most of the focus.

A universe which expands forever, or which expands faster in the later universe, makes a mess of this sort of approach to calculating a gravitational potential energy. So does any apparent recession velocity that's a large fraction of c (inducing significant redshift, whatever the recession (pseudo-)"force" might be).

However, the general idea is that there is a relationship between the kinetic energy a receding galaxy (in a system of coordinates -- a "frame" -- in which these kinematics appear) and a gravitational potential energy still occurs in a non-recollapsing universe. It's just that the potential energy climbs forever, and you get an equivalent to gravitational time dilation between galaxies at different gravitational potentials (i.e., between early-universe galaxies and higher-potential modern-times galaxies).

Accelerometers in galaxies will not show a cosmic acceleration for any galaxy; they're all really close to freely-falling (local galaxy-galaxy interactions are real -- collisions and mergers and close-calls happen -- but wash out over cosmological distances; look up "peculiar velocity" for details). Therefore we can conclude that there's no real force imposing acceleration on the galaxies. However that's also true of a cannonball in a ballistic trajectory, including one on an escape trajectory or one that enters into a stable orbit. Consequently one can draw some practical comparisons between a ballistic launch from Earth into deep space and galaxies spreading out from an initially denser early part of an expanding cosmos.

Dark energy as energy being extracted out of the universe

No, it's just a way of thinking about whatever is driving the expansion, and that doesn't dilute away with the expansion as ordinary matter and radiation does. It's not even a "real" energy in the sense that it is only an energy in the cosmological frame, and is a frame-dependent scalar quantity, whereas in the fuller theory it's just a multiplier of the metric tensor. So it's the full relativistic metric doing the work but we absorb some of that into cosmological coordinates in the cosmological frame of reference, carving up the metric tensor into a set of vectors including an expansion vector identical at every point in spacetime.

The expansion vector can also be thought of in terms of pressure: in a collapsing cosmological frame, a pressure drives galaxies together into a denser configuration. The inverse of pressure is tension, so in an expanding cosmological frame, it's a tension that pulls galaxies apart into a sparser configuration. (The reason one uses pressure or its inverse is that the matter fields are idealized as a set of perfect fluids at rest in the cosmological frame; each such fluid has an associated density and internal pressure which evolve with the expansion or contraction of the cosmos, generally becoming less positive in the time-direction of expansion (i.e., in the future direction in a universe like ours). Another way of thinking about pressure is as a measure of isotropic inflow of energy-momentum into a point; increasing pressure at a point therefore increases the curvature at that point. Tension is an isotropic outflow, and so positive tension is repulsive as opposed to the attraction from positive pressure.)

that explanation felt unsatisfactory to me

Hopefully the above helps a bit. Unfortunately there's only so much teaching one might do in a series of HN comments, and ultimately one probably is better served in developing some grounding in the full Einstein Field Equations / Friedmann-Lemaître equations before thinking in quasi-Newtonian ways. Going the other direction tends to lead to misunderstandings and developing false intuitions when running into situations where the quasi-Newtonian picture needs post-Newtonian correction terms.

It's cool that you have all sorts of questions. You could consider signing up for part time / non-business-hours courses in relativity at a nearby community college or the equivalent, depending on where you are, or maybe just bringing a hot lunch to a lecturer there in exchange for a quick informal tutorial. Anything like that is bound to get you to better answers than raising comments on HN threads about astrophysics in the broadest sense, as answers here are often somewhere between non-standard and unreliable.

Physicists (and in particular the subset doing physical cosmology) don't usually explore parametrizations of c because they're not clearly physical (and sometimes even clearly unphysical), or alternatively don't help solve astrophysical or cosmological problems.

Relativists sometimes like to explore things that make using the Tangherlini transformations rather than the Lorentz transformations look positively benign. (To be clear, the Tangherlini synchronization system is clearly unphysical, requiring infinite speeds. His thesis also proposed using a distinguished global frame, which is not really philosophically different from how the standard cosmological frame is used, and seems OK because the distribution of stress-energy can pick out useful systems of coordinates in standard relativity. Unfortunately his method frustrates and probably outright breaks comparisons between inertial reference frames related by a boost, which the standard cosmology does not, and it's hard to see an alternative method that preserves his central ideas.)

But why even be stuck with 3+1d spacetime like Tangherlini? He was trying to do physics. But an unphysical metric signature with 47 plusses and no minuses is really cool!

In our observed universe, FAPP, c is the same everywhere after recombination, and we get that from spectral lines. You have to play really weird games to preserve the Lyman-alpha forest's apparent isotropy while introducing spacetime (or redshift-space, here) anisotropy. Things like BAOs make the problem even harder.

If we strip away all that pesky radiation and the information its structure encodes, analysing variations of c gets a lot easier. A relatively recent paper (Lewis & Barnes 2021) I enjoyed considered anisotropy in the one-way speed of light in an FLRW cosmology with zero energy density (well, really the convenient Milne model, which is also far from spatially flat). "So far, we have considered two cases, where either the speed of light is isotropic, or the extreme case where the anisotropic speed is 1/2 in one direction, and infinite in the other. The question remains whether this holds true in general case, for an arbitrary κ": https://www.cambridge.org/core/journals/publications-of-the-... (arxiv: <https://arxiv.org/abs/2012.12037>). "For more general cosmological models, where the presence of mass and energy results in curved space-time, the picture is more complicated as there is no simple mapping of the modified Lorentz transformations into the general relativistic picture. We leave this discussion for a future contribution."

Sadly there doesn't seem to be a future contribution yet, at least going by published citations (<https://scholar.google.com/scholar?cites=2012575105829699847...>). (Of those, I've put the Chamberlain paper on my to-read pile; you'd appreciate how it relates to Tangherlini, "credence is given to one-way infinite light-speed inward to each particle in direct comparison against Einstein’s isotropic (c=constant) light-speed").

Of course there's also the excellent Magueigo 2003 VSL overview <https://iopscience.iop.org/article/10.1088/0034-4885/66/11/R...> copy <https://cds.cern.ch/record/618057/files/0305457.pdf> preprint <https://arxiv.org/abs/astro-ph/0305457>.

And even if you can make sense of an f(c) cosmology in the early visible universe, you will get to epochs before recombination and try to make sense of the later universe's chemistry, which of course relates to big bang light nucleosynthesis, baryogenesis and electroweak ssb. How do you abolish Lorentz symmetry in those epochs? Good luck!

(I mean, I think if you are doing physical cosmology you ought not to ignore gauge theory...)

No, there's no change in dimensionality.

The swapping of timelike and radial dimensions are a "game" frequently played with families of coordinates, including Schwarzschild coordinates. One can apply any system of coordinates on a physical system without changing the behaviour of the physical system: coordinates are unphysical. Think of navigating around in a neighbourhood: you can talk about going forward a few blocks then turning left, after which you go forward two more blocks; or for the same journey, going "city north" a few blocks then going "city west" two blocks. Here assuming that (initially) "forward" is in the "city north" direction (and "city north" is not necessarily exactly magnetic north nor a section of a meridian of longitude). After the left turn, "forward" is "city west". There's an analogue to the discussion's (ab)use of Schwarzschild coordinates.

In Schwarzschild spacetime, without applying any system of coordinates, just floating in free-fall far from a black hole extremizes your travel in the timelike dimension. (You can do this at home: you stay put at some point on Earth (whether you use GPS latitude/longitude/altitude or some other system of coordinates) but your wristwatch keeps ticking). Inside the black hole horizon, just floating in free-fall extremizes your travel in the direction of the singularity. Far from the black hole, accelerating as strongly as you can in any direction takes travel from the timelike dimension and puts it into one or more spatial dimensions. In particular, you have the freedom to increase the spacetime interval between you and the singularity. Within the horizon, however strongly you accelerate the spacetime interval between you and the singularity shrinks. This behaviour seems to invite the use a different set of coordinates applied to a patch of space around an observer far from the black hole and a patch of space around an observer inside the horizon. It's some human cognition thing, and in the early 20th century it took decades to discover systems of coordinates that work for observers far from the black hole, at the horizon, and inside the horizon. And even today, most people don't seem to try to enhance physical intuitions by swapping among arbitrary systems of coordinates (including no coordinates) on a single physical system like a black hole and a pair of observers (one inside the horizon and one far outside the black hole).

The Schwarzschild black hole interior is still locally Lorentz-invariant everywhere (because the whole Schwarzschild spacetime is a Lorentzian manifold).

The various local interactions of the Standard Model will keep working inside a black hole. In a really tiny patch around every point, everything behaves as if its in Minkowski space (flat 4-d (3 spatial + 1 time) spacetime).

(That's one of the problems of quantum field theory on curved spacetime: the "focusing-pressure" [for experts: this is encoded in the Weyl curvature tensor; my "scare quotes" take a view of this in a Raychaudhuri equation way] gets so high that the unknown ultraviolet behaviour of the Standard Model (a quantum field theory) becomes relevant. The Weyl behaviour in Schwarzschild is that quasispherical objects are strongly prolated with the long axis aligned radially: a soccer ball or basketball starts looking like an American or Canadian or Rugby football ball. The radial stretching "spaghettifies" by ripping apart weaker bonds (like intermolecular ones, and molecular ones, and ionizing atoms), but the tangential squashing ("focusing") must eventually generate more nuclear interactions, probably up to quantum chromodynamics (QCD) energies possibly before the radial stretching starts generating hadronization.

How this works in the Standard Model is just unknown. However simpler "test" quantum field theories (fewer, or even no, interactions; and often no colour-confinement-like processes) raise really difficult questions.

Finally, back to the Standard Model as local theory: how does any allegedly quantum nonlocality behaviour work? Local here in the sence that states can be distinguished by local measurements alone. Related questions: can you entangle particles deep inside a black hole? If an entangled pair fall in together, how does the entanglement evolve? Or obsessing black hole information people, what if you throw in only one half of an entangled pair and locally measure the outside half? Nobody has great answers for these sorts of questions at present, and there's no near-term hope of testing any proposals in laboratories or via astrophysical observation.

The practical sense is the binary-merger waveforms detected at LIGO, Virgo, and Kagra, which were emitted in the detectors' (and humanity's) past lightcones. We don't even have to consider "the ... future history of human race"; the gravitational-wave ringdown is from after the two horizons touched (and in particular the intermediate stage of the ringdown encodes the crossing of light from the light or photon ring structure around the not-yet-merged black holes into the final merged object, and the recapture of quite a lot of gravitational radiation scattered in the strong-gravity zone around the not-quite-in-contact binary).

Except in GR the math itself provides the reason why the part below the event horizon should be outside of our consideration

No it doesn't, and this has been known about since the 1920s (and reasonably understood since 1939 and well-understood since the early 1970s), and you can find out about this in any GR textbook, for example §12.2 of Wald, and problems 1 and 4 at the end of chapter 12. You should try solving those two exercises like any grad student (being sure to read problem 4 and to think about why it's asking for an upper limit) before making the sort of wrong claim about "the math itself" you made above.

A couple of things to understand: (1) in general black hole solutions do not superpose linearly [this is the thrust of problem 4]; (2) there are multiple lines of evidence supporting black hole mergers; (3) gravitational radiation is generic to any quasicircular orbit (not just black holes), with the emitted frequency and amplitude inversely proportional to the orbital diameter; (4) frequencies and amplitudes for some detections (e.g. GW150914) are too high for solid self-gravitating bodies anywhere in the sky.

You can't put a rock in a 100-millisecond orbit around the Earth; LIGO has ample data in the ~ 30 - 7000 Hz range. The gravitational wave ringdown of a neutron-star/neutron-star, neutron-star/black-hole, or black-hole/black-hole merger is totally unlike what one gets from a rock hitting the Earth.

The curves of rocks thrown in Earth's gravity don't become incomplete just because they transition from free-fall (geodesic motion) to accelerated (while resting on the surface). One can literally lift bits of meteorite out of craters. There's enough cosmic dust <https://en.wikipedia.org/wiki/Cosmic_dust> around launch sites that it's inevitable that some bits of meteorite have been taken back to space and are now in free-fall somewhere in or near the solar system (or as another possible example, some of the nickel or iridium in Voyager 1 components, if the ore was mined in Sudbury, Canada).

The curve of every part of a rock chucked through a black hole horizon ends inside the horizon. That curve-confinement is the characteristic feature of a black hole in General Relativity: no trapping surface, no black hole (Wald again, proposition 12.2.3). Where there is a trapping surface,no known high-energy behaviour of matter avoids collapsing gravitationally into a configuration in which every (non-spacelike) curve of the matter inside the horizon ends up becoming future-inextendible (that's what the singularity does: any curve touching it cannot be extended further within the horizon).

coordinate system so that infinities don't spoil our fun

Curvature scalars don't diverge just below the horizon of even a stellar-mass black hole. Coordinate divergence is not the same as curvature divergence, and different systems of coordinates on a single arrangement of mass can diverge at arbitrary radial distances, including very very large ones.

physics to philosophy

"Does the ringdown overtone of a merger of two black holes encode any of the accretion history of each black hole?" is a physical rather than philosophical question and is an avenue for testing solutions of the Einstein Field Equations (including approximate ones solved numerically) against astrophysical data. See for example https://www.ru.nl/en/research/research-news/the-observation-...

The National Film Board of Canada's documentary on black flies is an ear-worm: https://www.nfb.ca/film/blackfly/

everywhere in the universe

No, that's not correct. It only has to happen at one place in the spacetime, namely at the horizon itself. General Relativity is a theory of point-coincidences, after all.

Additionally there are ordinary observers (cosmic microwave background radiation, in particular) on hyperbolic trajectories grazing the infall point; there are observers ultraboosted towards the black hole; and there are observers orbiting other black holes whose proper time is less tilted with respect to a free-falling infaller than your proper time is.

The key point is that one obtains the free-faller's geodesic by solving the EFEs in the block spacetime, and one notes that some of that geodesic is outside the black hole, some of it is inside the black hole, and that portion inside the black hole at no point in the future exits the black hole (barring complete evaporation that allows the infaller's worldline to be extended outside the black hole, in which case there isn't an event horizon but there's still an apparent horizon and probably other trapping surface structure).

Solutions of the Einstein Field Equation give rise to the geodesic equation for each such solution. In an exact, analytical solution like Schwarzschild or Kerr, every geodesic is solved for the whole spacetime. The spacetime is a block universe, and one can pick out individual geodesic worldlines as a sort of thread that runs from the infinite past to the infinite future. The most interesting worldlines are lightlike and timelike geodesics; the latter are those which a physical observer (with mass) would follow in eternal free-fall. Timelike geodesics have the property that the time dimension is longest dimension of their thread-like presence in the block spacetime.

So far there are no coordinates in place at all. There's just talk of a block fully described by a system of differential equations. We can then proceed to apply coordinates to the block, and can use any coordinates that we might want. No choice of coordinates can change the geodesics through the block, only the way in which they talk about it. For instance, let's look at using different 2-d coordinates on the a restaurant where you and a friend are looking at each other across a dinner table. One could say you are north of the friend looking south, or your friend is in front of you looking back at you, or you are in front of your friend and looking back at him. Someone else in the restaurant could say that you are to the left of your friend, or that you are slightly northeast and your friend slightly southeast; a different person elsewhere in the restuarant could describe it exactly opposite: you are to the right, your friend to the left. And so on. But you aren't actually moving around the table or restaurant: the configuration of you and your friend isn't changed as we apply different sets of coordinates. And we can move the origin of Cartesian or polar or whatever coordinates anywhere in the restaurant, so you're at x=0,y=0 and your friend is displaced in the y direction. Or you're bothed displaced in x and y from the x=0,y=0 preferred by an onlooking diner at a different table.

In a black hole spacetime, there are geodesics which are interior to a set of horizons: once they cross such a horizon they stay crossed. It does not matter at all what the coordinates are that are used to describe the horizons or the geodesics.

relative to us

This is just you applying your coordinates to a block.

Doing so doesn't change the geodesics which cross a horizon in one direction only: their eternal past might be "free" but their eternal future is within the horizon.

time dilation relative to us

Again, this is applying "our" coordinates. However even those might differ: you are probably thinking in terms of the standard Schwarzschild coordinates or something close to them, whereas I might reach for Kruskal coordinates instead, which absorb timing differences. Just like someone in the restaurant might prefer north-south/east-west coordinates instead of a personal left-right/foreground-background system.

theoretical black holes

Well, yes, we assume General Relativity is sufficiently correct that astrophysical candidates are compared to black hole solutions in General Relativity rather than something different in a different theory.

We also make some simplifying assumptions which are known to be nonphysical but which represent very minor perturbations of black hole solutions to the Einstein Field Equations. Otherwise we would have no hope of calculating anything, and could not even approximate astrophysical candidates' behaviour.

Never as measured by our clocks

There's nothing special about our clocks. That seems to be the problem you are wrestling with.

You could get a hyperbolic clock on your smartwatch that slows down as you age, and ultimately becomes so slow that a tick on your wristwatch is more than long enough for a free-falling body to cross a black hole horizon. The physics doesn't change; the free-falling body's worldline in the block universe has a portion outside the horizon and a larger portion inside the horizon. You're just using different algorithms on your wristwatch to apply timelike coordinates to a part of that free-falling body's worldline.

Because one can use any sort of coordinates on a block universe with a set of solved-by-the-equations worldlines (or at least timelike and lightlike geodesics reasonably near a subsystem of interest) one can make poor choices about what set of coordinates to apply to a particular subsystem of the block universe. "Our [linear] clocks" is a poor choice for describing systems with strong gravitation, speeds comparable to c, strong acceleration, or any combination of those, because there is always a nontrivial element of hyperbolicity in such systems' worldlines. The hyperbolicity comes from the geometry of the spacetime, and is always there in any Lorentzian spacetime (meaning it has 3 spacelike and 1 timelike dimension where the latter is related to the former in line elements by the constant c and a change of sign).

Ok, what I take from your comment is that you're identifying General Relativity with certain solutions of GR's Einstein Field Equations. That's like deciding that algebra is just a handful of popular equations.

(Aside, I have run out of time for an editing pass on this comment, so hopefully I didn't leave in ridiculous typos or whatever).

Firstly, let's restrict ourselves to General Relativity as a physical theory. That means we don't have arbitrarily many dimensions with wild metric signatures. We have three spatial and one timelike dimension, so take a metric signature of (+,-,-,-) or (+,+,+,-) which are equivalent but end up with things being written down in different form. That's as opposed to (+,+,+,+,+,+) or (+,+,-,-), all of which can be studied using Einstein's mathematics. Indeed, it's popular particularly among quantum gravity people to work with fewer dimensions (+,+,-) or (+,-) or to go from a Lorentzian (and thus semi-Riemannian) manifold (+,+,+,-) to a Euclidean (Riemannian) one (+,+,+,+). "Quantum gravity people" here include Hawking and 't Hooft. (duck duck go or wikipedia search "Metric signature" for more)

General Relativity as a physical theory of gravitation in our universe 3-spatial-dimension-and-one-time-dimension admits all sorts of really weird spacetimes which are wildly wildy unlike anything in our universe. (In fact relativists have over the decades invented energy conditions in an attempt to remove a few "wildly"s from consideration as possible physical systems: if your spacetime doesn't fulfil some energy conditions everywhere in it, your spacetime is probably not a good match to systems in our universe. For instance, one energy condition requires that energy-density is nowhere negative; another requires that energy is nowhere observed to flow faster than c.) (search term here is "energy condition").

There are a few books worth of exact, analytical solutions to the Einstein Field Equations (those equations define a whole spacetime), some of which resemble astrophysical systems. One such 700-page non-exhaustive book: <https://www.cambridge.org/core/books/exact-solutions-of-eins...>. However there are many many more approximate solutions which have no closed form solution: that's the realm of numerical relativity.

The Schwarzschild black hole spacetime is an example of an exact analytical solution. But there is no superposition of such spacetimes available in General Relativity, so two Schwarzschild black holes in the same universe is not just some linear combination -- instead, we have approximate solutions which can only be solved numerically. That's just with the external properties of black holes: their horizon structures, at least when studying the gravitational waves such systems emit in their last bunch of orbits before merger. It doesn't matter what's inside the horizons for that.

Likewise, where isolated astrophysical black holes give us data is outside the horizon -- what's inside is pretty much irrelevant.

So, the exterior part of an exact solution like Kerr-Newman, with some small perturbations, is at least soluble such that the perturbed KN is an excellent approximation of astrophysical observations of black holes. However we have no observations of the interior part of any black hole, so no way of knowing if Kerr-Newman's interior is wildly unphysical!

(In fact Roy Kerr has said from time to time that because of the presence of matter inside a Kerr BH, the interior part of the solution he arrived at for spinning black holes is probably wrong, even though the exterior part is a remarkably good basis for modelling astrophysical black holes. An example is in his excellent 2016 talk which you can find on youtube at <https://youtu.be/nypav68tq8Q?t=2880> immediately after the 48 minute mark of the video and again at 49:20, however he develops that theme and repeats that point across much of the talk.)

The repair of an unphysical black hole interior might be to stitch together (using a thin-shell method like Darmois-Israel) the physically useful external Kerr solution with something very different inside the horizon but which is more physical. That is not the same, at all, as declaring General Relativity wrong!

Why would one do this? As Kerr implies, there are several invariants ("symmetries") of black hole solutions which are broken by the presence of matter on either side of the horizon. Is the inside part of the Kerr solution fragile to perturbations by matter? That's a work in progress. The outside is pretty clearly stable to such perturbations, mathematically: if you throw in a blob of gas, or star, or shine a very bright light at it, or throw some gravitational waves in its direction, the outside departs from Kerr for a time but soon enough returns to being very well modelled by a Kerr solution with different mass and/or spin. The stability of the inside is not settled. So maybe matter's presence forces a departure from the interior Kerr solution to something else inside, with the Kerr solution remaining in place outside.

Stitching together metrics is something we do all the time. One puts a collapsing patch of spacetime representing a galaxy cluster (in which things tend to move towards the centre, which is where one finds ginormous elliptical galaxies), or a black hole, into a an expanding cosmology (where one finds galaxy clusters flying away from one another) using methods like this. It's all GR, it's just not one single metric line element everywhere.

Of course, there might not be a useful set of metrics that covers the whole of a black hole spacetime, because some region (e.g. near the singularity) demands a theory that differs from General Relativity. For example, the coupling between gravitation and matter might "de-universalize" near the singularity, with some matter moving differently (in particular not falling inwards) compared to matter that moves on GR's trajectories, perhaps because they couple to an auxiliary gravitational field that is so weak away from the centres of black holes that it's never noticed. (This is one approach taken by people who attempt to build relativistic MOND: when gravity is at its weakest, one gets a strengthening of an auxiliary field). [auxiliary here means in addition to the metric tensor, e.g. a vector field on the left hand (curvature) side of the Einstein Field Equations].

However there is no reason from astronomers to prefer alternative theories over General Relativity. The presence of singularities inside black holes might depend on our present toolkit of exact analytical black hole solutions, which are almost all matter-free (vacuum solutions).

Down that line of thinking is confrontation with the work of Penrose and others that shows that singularities are found pretty generically in 3+1d General Relativity. And that's a topic for another time.