# Can black holes with the same mass evaporate with different speeds?

I am curious about the following observations:

(1) For a normal Schwarzschild black hole, it evaporates according to $dm/dt=-1/m^2$;

(2) We have eternal black holes which do not evaporate (though only a thought extreme case);

(3) Their difference is the microscopic state of the black hole(an eternal black hole is maximally entangled with another black hole in the sense that the density matrix of the black hole is I with a dimension of $2^{m^2}$).

So we have two extreme cases, either 'definitely evaporate following the fixed $m^3$ rule' or 'never evaporate' following '0 speed rule'.

Then due to continuity, the real world should allow the intermediate case, that is, black holes that evaporates with a speed between $m^3$ rule and 0 speed, depending on how a black hole is entangled with another black hole. For example, may it be possible to add some mass to eternal black holes to trigger it's evaporation?

It seems that this goes to the ER=EPR idea. According to Susskind, a single black hole has a 'bridge to nowhere' and it evaporates; for eternal black holes the double sided ER bridge between the maximally entangled black hole pairs has a maximal radius and they do not evaporate. Then how about the case where there is only a narrow ER bridge between two partially entangled black holes? Will they have different evaporation speeds depending on the ER bridge sizes?

Note: A simple idea on why normal black hole evaporates is that, if the evolution of the black hole is unitary, then the entanglement between subparts of a black hole will increase with time till saturate, so the 'bridge to nowhere' attached to a normal black hole is not dense enough at the beginning period of the black hole formation procedure, like a leaky basket, this allows the possibility of black hole evaporation. But for the eternal black holes, the entanglement always saturates, so the bridge is always dense and the spacetime basket holds water, then the eternal black holes can not evaporate.

But if the black hole pairs are not initiated from 'maximally entangled' states but from a 'partially entangled' state, then the 'basket bottom' will be denser than normal black hole but sparser than the eternal black hole case, then will it evaporate with a different speed?

• Eternal black holes only exist in classical general relativity. Once quantum mechanics is introduced (which needs to be done in order to talk about black hole evaporation), then eternal black holes do not exist. – Prahar Feb 11 '16 at 8:04
• Can you provide a reference for the claim that maximally entangled black holes do not evaporate? I am unfamiliar with this idea. – John Rennie Feb 11 '16 at 8:14
• @Prahar Do you mean the eternal black holes that Maldacena talked in 'Eternal black holes in Anti-de-Sitter'? – XXDD Feb 11 '16 at 8:16
• @John Rennie 'Eternal black holes in Anti-de-Sitter' (arXiv:hep-th/0106112v6), my understanding is that such kind of maximally entangled black hole pairs will not evaporate. I hope I am not totally wrong. – XXDD Feb 11 '16 at 8:20
• @John Rennie Maybe this paper also says something about it. 'Cool horizons for entangled black holes' arXiv:1306.0533v2. I am interested in the black hole information from a computer science point of view, not very familiar with black hole itself. So if I am totally wrong, please correct me. – XXDD Feb 11 '16 at 8:23