Black Hole from Entropy Maximization

TL;DR

This paper investigates the idea that black holes can be characterized by entropy maximization, deriving a self-gravitating quantum condensate configuration without a horizon that aligns with the Bekenstein-Hawking entropy.

Contribution

It introduces a novel semi-classical solution for highly excited matter configurations that maximizes entropy and matches black hole entropy without forming a horizon.

Findings

Derived a self-consistent, horizonless configuration with maximum entropy.

Showed the maximum entropy matches the Bekenstein-Hawking formula.

Established a bound on thermodynamic entropy consistent with the Bousso bound.

Abstract

One quantum characterization of a black hole motivated by (local) holography and thermodynamics is that it maximizes thermodynamic entropy for a given surface area. In the context of quantum gravity, this could be more fundamental than the classical characterization by a horizon. As a step, we explore this possibility by solving the 4D semi-classical Einstein equation with many matter fields. For highly-excited spherically-symmetric static configurations, we apply local typicality and estimate the entropy including self-gravity to derive its upper bound. The saturation condition uniquely determines the entropy-maximized configuration: self-gravitating quanta condensate into a radially-uniform dense configuration with no horizon, where the self-gravity and a large quantum pressure induced by the curvatures are balanced and no singularity appears. The interior metric is a self-consistent and non-perturbative solution in Planck's constant. The maximum entropy, given by the volume integral of the entropy density, agrees with the Bekenstein-Hawking formula through self-gravity, deriving the Bousso bound for thermodynamic entropy. Finally, 10 future prospects are discussed, leading to a speculative view that the configuration represents a quantum-gravitational condensate in a semi-classical manner.