Question

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

Answer 1

I am curious about the following observations:

(1) For a normal Schwarzschild black hole, it evaporates according to dm/dt=−1/m2dm/dt=−1/m2;

(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 2m22m2).

So we have two extreme cases, either 'definitely evaporate following the fixed m3m3 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 m3m3 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.

Answer 2

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Black holes are objects so compact and so dense that in their vicinity, the escape velocity exceeds the speed of light : their gravitational attraction traps even the light which ventures too close and is then lost.
However S. Hawking showed in the ’70s that the black holes are not so black eventually. They have an entropy, which can only increase, and thus a temperature : the black holes emit particles and thermal " radiation ", with a temperature which depends only on their mass : the black hole is the more " hot " that it is not very massive.
These particles are emitted in a zone right outside the horizon of the black hole (limit inside which nothing can escape). It is a quantum effect, based on the spontaneous creation of pairs of particle-antiparticles in the energy fluctuations of the vacuum.

Black holes of a fewsolar masses, residues of massive stars after their death, have a temperature quite lower than the cosmic background radiation and do not evaporate.

On the other hand, the microscopic black holes formed very early in the Universe already evaporated if their mass is lower than the billion tons. In the intermediate mass range, it could exist very hot black holes, still evaporating today.
At the time of the final phases of evaporation, the mass of the black hole becomes infinitely small, and thus its temperature tends towards infinity. The black hole disappears in a fantastic explosion.

The microscopic black holes involving at the same time very strong gravity and quantum mechanics, should be explained within the framework of a quantum theory of gravity, which today is not established yet. The string theory is among the best candidates for that theory, which should also unify all the forces.

This theory generalizes the individual elementary particles (with zero dimension to some extent) by particles with a dimension 1, the strings, at very high energy. The various modes of vibration of the strings correspond to various particles of different mass and energy.

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