Self-Gravity and Bekenstein-Hawking Entropy

TL;DR

This paper investigates how self-gravity influences entropy in black hole-like configurations by solving the semi-classical Einstein equations, showing that strong self-gravity can lead to an area-law entropy consistent with Bekenstein-Hawking formula.

Contribution

It provides a non-perturbative, self-consistent solution demonstrating the entropy follows the area law even with strong self-gravity, offering insights into quantum black holes.

Findings

Entropy follows the area law in strong self-gravity regimes.

Interior behaves like a local thermal state due to particle creation.

Self-gravity alters entropy from volume to area law.

Abstract

We study the effect of self-gravity on entropy by directly solving the 4D semi-classical Einstein equation. In particular, we focus on whether the Bekenstein-Hawking formula holds when self-gravity is extremely strong. As an example, we consider a simple spherically symmetric static configuration consisting of many quanta and construct a self-consistent non-perturbative solution for $\hbar$ in which the entropy exactly follows the area law for many local degrees of freedom of any kind. This can be a candidate for black holes in quantum theory. It represents a compact dense configuration with near-Planckian curvatures, and the interior typically behaves like a local thermal state due to particle creation. Here, the information content is stored in the interior bulk, and the self-gravity plays an essential role in changing the entropy from the volume law to the area law. We finally discuss implications to black holes in quantum gravity and a speculative view of entropy as a gravitational charge.