Gauss-Codazzi thermodynamics on the timelike screen
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2L 2Y5 (Canada)
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. The latter requirement can be weakened by asking that the extrinsic curvature, if present at the beginning, evolves in time like on a cone and just rescales proportionally to the expansion.
- OSTI ID:
- 21432375
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 82, Issue 8; Other Information: DOI: 10.1103/PhysRevD.82.084004; (c) 2010 American Institute of Physics; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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