Apparent horizons, black hole entropy and loop quantum gravity

TL;DR

This paper discusses black hole entropy in loop quantum gravity, highlighting that the entropy calculation applies broadly, clarifying the phase space constraints involved, and confirming the area-proportionality of entropy.

Contribution

It clarifies the applicability of entropy calculations to general covariant theories and distinguishes the relevant phase space constraints in loop quantum gravity.

Findings

Entropy calculation applies to theories without black hole solutions.

The used phase space constraint is not the apparent horizon equation.

A different phase space constraint implies entropy is proportional to surface area.

Abstract

In recent work on black hole entropy in non-perturbative quantum gravity, an action for the black hole sector of the phase space is introduced and (partially) quantized. We give a number of observations on this and related works. In particular we show that (I) the entropy calculation applies without change to generally covariant theories having no black hole solutions, (II) the phase space constraint used to select the black hole sector is not the apparent horizon equation, which is the natural phase space constraint separating trapped and untrapped regions on an initial data surface, and (III) there appears to be at least one other phase space constraint which leads to the conclusion that the entropy associated with a bounding two-dimensional surface is proportional to its area.