The double doors of the horizon

Abstract

In statistical mechanics entropy is a measure of disorder obeying Boltzmann's formula S = log N , where N is the accessible phase space volume. In black hole thermodynamics one associates to a black hole an entropy Bekenstein-Hawking SBH . It is well known that SBH is very large for astrophysical black holes, much larger than any collection of material objects that could have given rise to the black hole. If SBH is an entropy the question is thus what is the corresponding N , and how come this very large phase space volume is only opened up to the universe by a gravitational collapse, which from another perspective looks like a massive loss of possibilities. I advance a hypothesis that the very large increase in entropy can perhaps be understood as an effect of classical gravity, which eventually bottoms out when quantum gravity comes into play. I compare and discuss a selection of the very rich literature around these questions.

On Black Hole Thermodynamics, Singularity, and Gravitational Entropy

“…In other words, the initial states that form the black hole saturates the Bekenstein-Hawking entropy. This is non-generic: a typical collapse of a stars to form a black hole, for example, involves a huge increase of entropy by a factor of 10 20 (M/M ) 1/2 , where M denotes a solar mass [106,107]. While specific examples can be constructed at the classical level whose initial conditions do saturate the Bekenstein-Hawking entropy bound, such configurations are highly nontrivial and finely tuned [108].…”