Notes on Entropy Force in General Spherically Symmetric Spacetimes

TL;DR

This paper demonstrates how gravity can be interpreted as an entropy force in general spherically symmetric spacetimes, especially at trapping horizons, extending Verlinde's ideas to Einstein's equations.

Contribution

It generalizes the concept of gravity as an entropy force to Einstein's equations in spherically symmetric spacetimes, focusing on trapping horizons and including matter effects.

Findings

Entropy change at trapping horizons can be identified with an entropy force.

Heat flux from matter fields influences entropy change.

Surface gravity determines the entropy force at horizons.

Abstract

In a recent paper [arXiv:1001.0785], Verlinde has shown that the Newton gravity appears as an entropy force. In this paper we show how gravity appears as entropy force in Einstein's equation of gravitational field in a general spherically symmetric spacetime. We mainly focus on the trapping horizon of the spacetime. We find that when matter fields are absent, the change of entropy associated with the trapping horizon indeed can be identified with an entropy force. When matter fields are present, we see that heat flux of matter fields also leads to the change of entropy. Applying arguments made by Verlinde and Smolin, respectively, to the trapping horizon, we find that the entropy force is given by the surface gravity of the horizon. The cases in the untrapped region of the spacetime are also discussed.