Maximum Entropy Principle for Self-gravitating Perfect Fluid in Lovelock Gravity

TL;DR

This paper explores the connection between gravity and thermodynamics in Lovelock gravity by deriving a TOV-like equation from the maximum entropy principle for a static perfect fluid system.

Contribution

It demonstrates that the TOV equation in Lovelock gravity can be derived from the maximum entropy principle, extending the thermodynamic-gravity connection beyond Einstein gravity.

Findings

Derived a generalized mass function in Lovelock gravity.

Established that the TOV-like equation follows from the maximum entropy principle.

Showed a deep link between thermodynamics and gravity in higher-order gravity theories.

Abstract

We consider a static self-gravitating system consisting of perfect fluid with isometries of an $(n-2)$-dimensional maximally symmetric space in Lovelock gravity theory. A straightforward analysis of the time-time component of the equations of motion suggests a generalized mass function. Tolman-Oppenheimer-Volkoff like equation is obtained by using this mass function and gravitational equations. We investigate the maximum entropy principle in Lovelock gravity, and find that this Tolman-Oppenheimer-Volkoff equation can also be deduced from the so called "maximum entropy principle" which is originally customized for Einstein gravity theory. This investigation manifests a deep connection between gravity and thermodynamics in this generalized gravity theory.