Notes on Entropy Force in General Spherically Symmetric Spacetimes

Details Notes on Entropy Force in General Spherically Symmetric Spacetimes Notes on Entropy Force in General Spherically Symmetric Spacetimes

2010-02-05

arxiv.org/abs/1002.1136v3

Phys.Rev.D81:084012,2010

Physics

High Energy Physics

High Energy Physics - Theory

revtex4, 21 pages, no figures, one reference added, published version, to appear in Phys.Rev.D

Scientific paper

10.1103/PhysRevD.81.084012

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.

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