Black Holes: Thermodynamics, Information, and Firewalls by Robert B. Mann

Author:Robert B. Mann
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Brick Wall Model The idea here is that there is a gas of quanta forming a thermal atmosphere near the black hole, whose entropy is the entropy of the black hole [122]. This atmosphere is prevented from making contact with the horizon via a boundary condition referred to as a “brick wall” [123]. The entropy is found to be proportional to the horizon area, but with infinite coefficient, and so a renormalization of sorts is required here as well. This approach works in any dimension [124].

Entropy of entanglement An external observer cannot access the interior state of the black hole, so the only meaningful exterior quantum states are reduced states for which the internal degrees of freedom have been traced out. In general the degrees of any quantum field external to the horizon should be entangled with those inside the black hole, and so even if the global state of the field was pure (and therefore of zero entropy), such reduced states will be mixed, with non-zero entropy. This entanglement entropy is indeed proportional to the horizon area (as required), but with a coefficient that diverges at short distance, requiring renormalization by physical arguments [125, 126].

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