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Gauss-Codazzi thermodynamics on the timelike screen · Around

2010

Gauss-Codazzi thermodynamics on the timelike screen

Piazza, Federico

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It is a known result by Jacobson that the flux of energy-matter through a local Rindler horizon is related with the expansion of the null generators in a way that mirrors the first law of thermodynamics.

We extend such a result to a timelike screen of observers with finite acceleration.
Since timelike curves have more freedom than null geodesics, the construction is more involved than Jacobson's and few geometrical constraints need to be imposed: the observers' acceleration has to be constant in time and everywhere orthogonal to the screen.
Moreover, at any given time, the extrinsic curvature of the screen has to be flat.

Built on

J. D. Bekenstein, “Black holes and entropy,” Phys. Rev. D 7
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Earlier work this paper cites.
J. M. Bardeen, B. Carter and S. W. Hawking, “The Four laws of black hole mechanics,” Commun. Math. Phys. 31
1973
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S. W. Hawking and G. F. R. Ellis, “The Large scale structure of space-time,” Cambridge University Press, Cambridge, 1973
1973
Earlier work this paper cites.
E. Poisson, “A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics,” Cambridge University Press, Cambridge, 1973
1973
Earlier work this paper cites.

Similar

T. Jacobson, “Thermodynamics of space-time: The Einstein equation of state,” Phys. Rev. Lett. 75
1995
Cited alongside, same era.
A. V. Frolov and L. Kofman, “Inflation and de Sitter thermodynamics,” JCAP 0305
2003
Cited alongside, same era.
A. Ashtekar and B. Krishnan, “Dynamical horizons and their properties,” Phys. Rev. D 68
2003
Cited alongside, same era.
R. G. Cai and S. P. Kim, “First law of thermodynamics and Friedmann equations of Friedmann-Robertson-Walker universe,” JHEP 0502
2005
Cited alongside, same era.
E. P. Verlinde, “On the Origin of Gravity and the Laws of Newton,” arXiv:1001.0785 [hep-th]
Original
Cited in the paper.
F. Piazza, “New views on the low-energy side of gravity,” arXiv:0910.4677 [gr-qc]
Original
Cited in the paper.
O. Dreyer, “Emergent general relativity,” arXiv:gr-qc/0604075
Original
Cited in the paper.

Then

S. Cacciatori, F. Costa and F. Piazza, “Renormalized Thermal Entropy in Field Theory,” Phys. Rev. D 79
Original
2009
Later among the works it cites.
T. Padmanabhan, “Gravity and the thermodynamics of horizons,” Phys. Rept. 406
Original
2010
Closest in time.
P. Nicolini, “Entropic force, noncommutative gravity and ungravity,” Phys. Rev. D 82
Original
2010
Closest in time.
F. Piazza, “Glimmers of a pre-geometric perspective,” Found. Phys. 40
2010
Closest in time.

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