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The thermodynamic structure of Einstein tensor · Around

2010

The thermodynamic structure of Einstein tensor

Kothawala, Dawood

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We analyze the generic structure of Einstein tensor projected onto a 2-D spacelike surface S defined by unit timelike and spacelike vectors u_i and n_i respectively, which describe an accelerated observer (see text).

Assuming that flow along u_i defines an approximate Killing vector X_i, we then show that near the corresponding Rindler horizon, the flux j_a=G_ab X^b along the ingoing null geodesics k_i normalised to have unit Killing energy, given by j .
k, has a natural thermodynamic interpretation.
Moreover, change in cross-sectional area of the k_i congruence yields the required change in area of S under virtual displacements \emph{normal} to it.

Built on

R. M. Wald, General Relativity
1984
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T. Dray, G. ’t Hooft, The gravitational shock wave of a massless particle
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T. Jacobson, Thermodynamics of Spacetime: The Einstein Equation of State
1995
Earlier work this paper cites.
S. Hayward, Unified first law of black-hole dynamics and relativistic thermodynamics
1998
Earlier work this paper cites.
T. Padmanabhan, Classical and Quantum Thermodynamics of horizons in spherically symmetric spacetimes
2002
Earlier work this paper cites.

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Then

M. Parikh, S. Sarkar, arXiv:0903.1176; T. Padmanabhan, arXiv:0903.1254; R. Brustein, M. Hadad, Phys. Rev. Lett
Original
2009
Later among the works it cites.
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