# Entropy of Self-Gravitating Anisotropic Matter

## TL;DR

This paper explores the thermodynamic entropy of self-gravitating anisotropic matter in general relativity, demonstrating the link between gravitational field equations and thermodynamics, and calculating entropy for objects like stars and wormholes.

## Contribution

It introduces a method to derive gravitational equations from entropy considerations for anisotropic matter, confirming the gravity-thermodynamics correspondence.

## Key findings

- Variational entropy reproduces Einstein's equations for anisotropic matter.
- Entropy calculations for compact stars and wormholes are presented.
- The approach supports the thermodynamic interpretation of gravity.

## Abstract

We examine the entropy of self-gravitating anisotropic matter confined to a box in the context of generalrelativity. The configuration of self-gravitating matter is spherically symmetric, but has anisotropic pressure of which angular part is different from the radial part. We deduce the entropy from the relation between the thermodynamical laws and the continuity equation. The variational equation for this entropy is shown to reproduce the gravitational field equation for the anisotropic matter. This result re-assures us the correspondence between gravity and thermodynamics. We apply this method to calculate the entropies of a few objects such as compact star and wormholes.