Gauss-Codazzi thermodynamics on the timelike screen

Abstract

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.

8+1 pages, final version

References in corpus (7)

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Cited by in corpus (7)

• Lessons from Classical Gravity about the Quantum Structure of Spacetime
• Einstein's Equations from the Stretched Future Light Cone
• First law of thermodynamics on holographic screens in entropic force frame
• `Thermodynamics' of Minimal Surfaces and Entropic Origin of Gravity
• Eternal inflation and a thermodynamic treatment of Einstein's equations
• The Einstein equation of state as the Clausius relation with an entropy production
• Gravitational thermodynamics and universal holographic duality in dynamical spacetimes