Thermodynamic structure of gravitational field equations

Abstract

There is an intriguing analogy between the gravitational dynamics of horizons and thermodynamics, which is not yet understood at a deeper level. In fact, it has been shown for several cases that the on-horizon structure of the gravitational field equations in Einstein theory have the structure of first law of thermodynamics. In this talk, we discuss how such a structure arises and show that the field equations near any static horizon can be written as: TdS − dE = PdV . Moreover, the result extends beyond Einstein theory and holds for Lanczos-Lovelock lagrangians as well. The entropy S we obtain is precisely the Noether charge entropy of Wald, and E provides a natural generalization of quasi-local energy of the horizon. We comment on several implications of this result, particularly the notion of gravitational entropy [treated as the Noether charge of diffeomorphism invariance] associated with horizons and it's role in gravitational dynamics arising out of virtual displacements of the horizon.