Gravitational entropy and thermodynamics away from the horizon

We define, by an integral of geometric quantities over a spherical shell of arbitrary radius, an invariant gravitational entropy. This definition relies on defining a gravitational energy and pressure, and it reduces at the horizon of both black branes and black holes to Waldʼs Noether charge entrop...

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Bibliographic Details
Published in:Physics letters. B 2012-08, Vol.715 (1-3), p.267-270
Main Authors: Brustein, Ram, Medved, A.J.M.
Format: Article
Language:English
Subjects:
Elementary particles
Energy (nuclear)
Entropy
Equivalence
Exact sciences and technology
Field theory
Horizon
Invariants
Nuclear physics
Physics
The physics of elementary particles and fields
Thermodynamics
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Summary:We define, by an integral of geometric quantities over a spherical shell of arbitrary radius, an invariant gravitational entropy. This definition relies on defining a gravitational energy and pressure, and it reduces at the horizon of both black branes and black holes to Waldʼs Noether charge entropy. We support the thermodynamic interpretation of the proposed entropy by showing that, for some cases, the field theory duals of the entropy, energy and pressure are the same as the corresponding quantities in the field theory. In this context, the Einstein equations are equivalent to the field theory thermodynamic relation TdS=dE+PdV supplemented by an equation of state.
ISSN:0370-2693
1873-2445
DOI:10.1016/j.physletb.2012.07.051