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As far as I had learned, the laws of physics are time reversible (except perhaps by a few decay processes). This is usually illustrated by saying that you can reverse a movie and still get a possible physical process. The movie can look weird at the macroscopic level because of the second law. Thus even if uncracking an egg looks weird, it is still physically possible (that is, it does not violate any fundamental physical laws).

Is this also true about black holes? can you reverse a movie of a black hole formation and get a plausible (although highly unlikely) process? My guess is that you cannot, but I am not sure what fundamental law would be violated, or what makes general relativity time irreversible.

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It is the second law of Black Hole thermodynamics. Black Holes (BH) can only have their entropy stay the same or increase. A BH splitting into 2 would violate that.

BH entropy is proportional to the area of the horizon S ~ A, while the area is proportional to the horizon radius square, and the horizon radius (how far away from the center singularity) is proportional to its mass. So S ~ $M^2$. This is for a Schwarzschild BH. For a Kerr BH it's more complex involving the angular momentum, and if charged the charge also, but the results are similar.

As in the comment on Is there a way to split a black hole? in 2012, since $(m_1 + m_2)^2$ > $m_1^2 + m_2^2$, the end entropy is smaller than the starting entropy. Entropy decreases. That is impossible in BH thermodynamics. This is for Schwarzschild BH, a similar calculation is possible for Kerr and charged Kerr BHs (I've done the calculations for those to get the max grav radiation emitted, but not the other way around to prove they can't split, but I think it's tRue also). It is proven in one of the answers to the question in the 2012 reference above.

In all cases it also requires that energy is conserved, i.e., that there was not an external insertion of energy. If you do then it is possible

The impossible cases are the opposite of binary BH mergers which are possible and do happen, as detected by LIGO on 9/14/15. That increased entropy, splitting or the inverse would not be possible. In fact Hawking used the formulas for entropy for also the charged Kerr BHs, and derived the maximum gravitational radiation permitted in all cases, since any gravitational radiation carries energy, i.e.,part of the original mass M of the BH, and if it carries away too much the resulting horizons get too small and are prohibited by the second law. See the LIGO merger detection at http://www.ligo.org/science/Publication-GW150914/index.php

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Bob Bee
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All kinds of crazy things are possible in GR if you don't make any assumptions about the nature of the stress-energy tensor. Physicists often impose various energy conditions on the stress-energy tensor reflecting our expectations about "physically realistic" types of matter. While the Einstein equations are invariant under time-reversal, the energy conditions might not be.

For example, Hawking proved that if the stress-energy tensor obeys the weak energy condition (WEC), then the total area of the event horizon(s) of a system of black holes can only increase . But even if a stress tensor obeys the WEC, then its time-reversed counterpart might not, and therefore would constitute "exotic" matter.

So an exact time-reversed version of a black hole collision is indeed allowed by Einstein's equations, but it might require exotic matter to "power" it. Outside the black hole, it might appear as a "negative mass" black hole or a white hole.

tparker
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A time-reversed black hole is a white hole (basically, a spacetime region that cannot be entered by any process), so your reversed movie would start looking weird before you even talk about any sort of splitting/disintegration/evaporation/whatever, because we don't observe white holes in nature, and it is belived that the white hole region of the extended Kruskal spacetime is cut off by boundary conditions.

Zo the Relativist
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