Black Hole Entropy in General Relativity

TL;DR

This paper presents a gauge-invariant, background-independent approach to black hole entropy in general relativity, reproducing the Bekenstein-Hawking formula and offering a new framework for semiclassical gravity.

Contribution

It introduces a gauge-invariant boundary condition framework that yields a background-independent action for black hole formation, advancing semiclassical gravity theory.

Findings

Reproduces the Bekenstein-Hawking entropy formula

Provides a background-independent action for black holes

Supports a phase-space volume quantization approach

Abstract

The Bekenstein-Hawking formula relates the black hole entropy and horizon area. Semiclassical entropy computations have relied on an action principle that fixes a gauge dependent and classically unobservable boundary three-geometry and renders elusive a precise physical notion of both energy and entropy in de Sitter backgrounds. Instead, we impose gauge invariant boundary conditions and report the background independent action for black hole formation. Assuming standard arguments for the relation between the action and entropy, we reproduce the Bekenstein-Hawking formula and motivate a quantization of the phase-space volume. This background independent approach applies to spacetimes of arbitrary energy density and enables a radically conservative framework for semiclassical gravity.