TY - JOUR

T1 - Gravitational entropy and thermodynamics away from the horizon

AU - Brustein, Ram

AU - Medved, A. J.M.

N1 - Funding Information:
The research of R.B. was supported by the Israel Science Foundation grant No. 239/10 . The research of A.J.M.M. received support from Rhodes University and the Claude Leon Merit Award grant No. CLMA05/2011 . A.J.M.M. thanks the Arnold Sommerfeld Center for Theoretical Physics at Ludwig-Maximilians-Universität München for their hospitality.

PY - 2012/8/29

Y1 - 2012/8/29

N2 - 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 Wald's 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.

AB - 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 Wald's 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.

UR - http://www.scopus.com/inward/record.url?scp=84865337992&partnerID=8YFLogxK

U2 - 10.1016/j.physletb.2012.07.051

DO - 10.1016/j.physletb.2012.07.051

M3 - Article

AN - SCOPUS:84865337992

VL - 715

SP - 267

EP - 270

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 1-3

ER -