Entropy density of spacetime and thermodynamic interpretation of field equations of gravity in any diffeomorphism invariant theory

Padmanabhan, T.
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I argue that the field equations of any theory of gravity which is diffeomorphism invariant must be expressible as a thermodynamic identity, TdS=dE around any event in the spacetime. This fact can be demonstrated explicitly (and rather easily) if: (a) one accepts the Noether current of the theory as providing the definition for local entropy density and (b) one is allowed to introduce the local notions of a Rindler frame, acceleration horizon and a Killing vector (related to translation in Rindler time) around any event. It is conceptually incorrect - in general - to invert this argument and obtain the field equations of the theory from the thermodynamic identity. I discuss under what conditions this may be possible. Several subtleties related to these arguments are described.
Comment: revtex; 5 pages; no figures
High Energy Physics - Theory, Astrophysics - Cosmology and Nongalactic Astrophysics, General Relativity and Quantum Cosmology