Friedmann Equations and Thermodynamics of Apparent Horizons

Abstract

With the help of a masslike function which has dimension of energy and equals to the Misner-Sharp mass at the apparent horizon, we show that the first law of thermodynamics of the apparent horizon $dE=T_{A}d{S}_A$ can be derived from the Friedmann equation in various theories of gravity, including the Einstein, Lovelock, nonlinear, and scalar-tensor theories. This result strongly suggests that the relationship between the first law of thermodynamics of the apparent horizon and the Friedmann equation is not just a simple coincidence, but rather a more profound physical connection.

no figures, V2: re-organized and re-writtend, main results and conclusion unchanged, Phys. Rev. Lett. in press

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