Thermodynamics of Spacetime: The Einstein Equation of State

Ted Jacobson
Phys. Rev. Lett. 75, 1260 – Published 14 August 1995
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Abstract

The Einstein equation is derived from the proportionality of entropy and the horizon area together with the fundamental relation δQ=TdS. The key idea is to demand that this relation hold for all the local Rindler causal horizons through each spacetime point, with δQ and T interpreted as the energy flux and Unruh temperature seen by an accelerated observer just inside the horizon. This requires that gravitational lensing by matter energy distorts the causal structure of spacetime so that the Einstein equation holds. Viewed in this way, the Einstein equation is an equation of state.

  • Received 23 May 1995

DOI:https://doi.org/10.1103/PhysRevLett.75.1260

©1995 American Physical Society

Authors & Affiliations

Ted Jacobson

  • Department of Physics, University of Maryland, College Park, Maryland 20742-4111

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Issue

Vol. 75, Iss. 7 — 14 August 1995

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