Area scaling entropies for gravitating systems

TL;DR

This paper investigates how the entropy of a self-gravitating, spherically symmetric matter system transitions from volume to area scaling as gravitational effects intensify, resembling black hole thermodynamics.

Contribution

It introduces a model showing how gravitational self-interactions alter entropy scaling laws, bridging the gap between ordinary matter systems and black hole thermodynamics.

Findings

Entropy scales with volume when gravity is negligible.

A correction term appears as gravity strengthens.

Entropy approaches area scaling near the event horizon.

Abstract

The entropy of a spherically symmetric distribution of matter in self-equilibrium is calculated. When gravitational effects are neglected, the entropy of the system is proportional to its volume. As effects due to gravitational self-interactions become more important, the entropy acquires a correction term and is no longer purely volume scaling. In the limit that the boundary of the system approaches its event horizon, the total entropy of the system is proportional to its area. The scaling laws of the system's thermodynamical quantities are identical to those of a black hole, even though the system does not possess an event horizon.