Black Hole Puzzle

"Moreover, even without invoking nonsingular models, it’s not clear that rotating or charged BHs form an event horizon at all when evaporation is taken into account."

Even this paper using modern (2024-era) numerical methods struggles to model the complexities of physically realistic black holes, and ends with a "... more research needed" at the end.

> Ginzburg & Frolov 1987

That was 37 years ago! We may have figured out one or two things about black holes since then.

I did. In particular I did not miss the whole preceding apparent horizon vs event horizon context of §VIII or the second half of the second column of p. 17, all of which conflicts with your:

  It hasn't finished forming because as its gravitational 
  field increases its time distortion increases. Its 
  formation is "frozen in time" (actually just very very 
  slow), it is *never fully formed*.

And then this choice statement and your previous paragraph in mixed order:

> That was 37 years ago! We may have figured out one or two things about black holes since then

"Tell all physicists you don't read physics papers without saying you don't read physics papers..." [1]

I mean, did you even look at the range of dates in your One Good Paper's bibliography?

For starters, Ginzburg & Frolov was just a useful foundational paper (which I suspected you had never heard of) that shows that generically in curved spacetimes, different observers count different numbers of particles, and in particular one observer's vacuum can be another observer's cloud of electrons, positrons, and photons. This was a nice way of saying that your "relativity does not allow observers to disagree on observations of what" is just wrong.

I gave you a google scholar link to the 37 year old paper paper so that it would be clear anyone with a slightly different academic background (and I hoped you) that it's a foundational theory paper. Frolov is the well-known author of two standard textbooks on the physics of black holes (with Novokov and with Zelnikov), both of which deal with Frolov's 37-year-old paper in the context of evaporation and of different observers counting different particle numbers and how that an acceleration between past and future observers accounts for Hawking quanta. Both Frolov textbooks appear early on the first page of google scholar results.

(The 37-year-old concern is especially funny. Frolov's 21st century textbook, like practically all textbooks on gravitational phenomena and theory, even reference papers which are now more than a hundred years old, oh no! Choosing a recent GR textbook -- Carroll 2014 -- the author lists under Advanced General Relativity: Hawking & Ellis 1973, de Felice & Clarke 1990, Sachs & Wu 1977; and in the Graduate section: Wald 1984, MTW 1973, Weinberg 1972, ...)

> modern (2024-era) numerical methods

which are built to be compatible with ... what? Analytical and/or perturbation theory, right?

(BTW, Stark & Piran published their computer results in 1985: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.55...>. Again, can be found by placing sci-hub.se/ before that URL. That's 39 years ago! "We have performed an extensive series of tests [including] known perturbation solutions.")

One more kick at the ridiculous dead horse: at the bottom of p. 17 one finds, "We are not the first to propose a picture like the one presented throughout this section. As far back as theoriginal discovery of the Hawking effect, similar ideas were invoked in [4], and by various comments of [2, 3]". The dates of those are respectively 1974, 1975, and 1976. Oh no!

Could it be that among the "one or two things about black holes since then" that "We" may have "figured out" is that early theory papers (the 80s are not early) turn out to have good support in things like astrophysics, magnetohydrodynamics, gravitational wave observations, Hulse-Taylor / PSR J0737−3039 etc. etc.?

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[1] https://journals.aps.org/125years but uh oh that was 2018 and surely the list would be totally different now!

Singleton black holes from collapsed stars move in their galaxy about the same as uncollapsed star: on the order of 200 km/s or so (faster towards the middle but still in the disc where motion is roughly circular around the galaxy's centre, slower in the bulge where motion is randomly around the galaxy's centre). Really unusually high-velocity stars move about 65-100 km/s faster than these, which is still not that fast, and "hypervelocity stars" (we've seen some twenty, compared to the 100 billion or so stars in our galaxy) move about only five to ten times faster still, but we're still at only about a thousandth of the speed of light.

Black hole binaries can be arbitrarily wide, even up to many thousands of light-years, taking hundreds of thousands of years or more to orbit each other, possibly at speeds comparable to those of stars in galaxies. MEERKAT just announced its pulsar timing array results which focuses on orbital periods of some tens of years ("nanohertz gravitational waves"), which means not moving very fast. Here's a nice cartoon: https://physics.aps.org/articles/v16/116 LIGO is sensitive to much higher frequencies, once a black hole binary's mutual orbit has shrunk considerably - at the final chirp, they are moving at double-digit percentages of the speed of light and the orbital periods are in the milliseconds. In that regime black hole horizons do have bumps raised on them: https://www.youtube.com/watch?v=Y1M-AbWIlVQ

The black holes can't rip apart though: everything inside stays inside.

I'm afraid I can't figure out what you're talking about in terms of frozen in time, time dilation, or atoms compacting.

That's incorrect. Energy conservation can be violated at a much smaller scale, e.g. when gravitational waves are involved, or redshift phenomena (e.g. in Schwarzschild).

Yes, we usually talk about the fact that gravitational waves can carry energy but what exactly is their energy content? And what exactly is the conservation equation here?

> Locally GR conserves energy the same as any other self-consistent physical theory.

Locally, you can write down a divergence equation for the energy momentum tensor, yes. However, locally we're in Minkowski space anyway, so that is not really surprising.

The point is that the local divergence equation doesn't take into account the energy carried by the gravitational field itself. To give another example beyond gravitational waves: A Schwarzschild black hole carries mass, even though it is a vacuum solution to the Einstein field equations.

See also https://en.m.wikipedia.org/wiki/Mass_in_general_relativity and in particular the section on quasi-local mass.