# What law prevents the disintegration (not evaporation) of a black hole?

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.

• You have to say "fundamental laws" since the second law of thermodynamics is obviously not time reversible. What will be "fundamental" for black holes, and whether it is time reversible, is unclear (quantum gravity?), but general relativity is not it, it breaks down near the event horizon. Even if black holes were entirely classical objects reversing the collapse would be so hhhighly unlikely that we might as well say that the second law prevents it. – Conifold Oct 28 '16 at 0:45
• You could ask the same question about the Earth. – Keith McClary Oct 28 '16 at 17:30

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.

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

• Thanks for your answer, I was not asking about splitting but about disintegrating, in the sense that after disintegration there is no black hole or singularity left (just reverse the movie of a forming black hole). And I am asking if something prevents this other than the second law (which does not prevent it, only makes it extremely unlikely)\ – user126422 Oct 28 '16 at 23:07
• No, I think it makes it impossible. Without an external source of energy and probably entropy the entropy would decrease which makes it impossible yes, the second law and the first on consevation of energy. I don't think there any other firm 'proof'. I'm talking about general relativity, not sure what quantum gravity may do, but those two laws seem to have held up even in the semi classical quantum Hawking effect. – Bob Bee Oct 29 '16 at 22:51

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.

## protected by Qmechanic♦Jan 6 '17 at 3:24

Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count).