Thermodynamics of Spacetime: The Einstein Equation of State

By regarding the Einstein equations as equation(s) of state, we demonstrate that a full cohomogeneity horizon first law can be derived in horizon thermodynamics. In this approach both the entropy and the free energy are derived concepts, while the standard (degenerate) horizon first law is recovered by a Legendre projection from the more general one we derive. These results readily generalize to higher curvature gravities and establish a way of how to formulate consistent bla...

We perform an analysis where Einstein's field equation is derived by means of very simple thermodynamical arguments. Our derivation is based on a consideration of the properties of a very small, spacelike two-plane in a uniformly accelerating motion.

It has previously been shown that the Einstein equation can be derived from the requirement that the Clausius relation dS = dQ/T hold for all local acceleration horizons through each spacetime point, where dS is one quarter the horizon area change in Planck units, and dQ and T are the energy flux across the horizon and Unruh temperature seen by an accelerating observer just inside the horizon. Here we show that a curvature correction to the entropy that is polynomial in the R...

A general formalism for understanding the thermodynamics of horizons in spherically symmetric spacetimes is developed. The formalism reproduces known results in the case of black hole spacetimes. But its power lies in being able to handle more general situations like: (i) spacetimes which are not asymptotically flat (like the de Sitter spacetime) and (ii) spacetimes with multiple horizons having different temperatures (like the Schwarzschild-de Sitter spacetime) and provide a...

It has recently been shown that the Einstein equation can be derived by demanding a non-equilibrium entropy balance law dS = dQ/T + dS_i hold for all local acceleration horizons through each point in spacetime. The entropy change dS is proportional to the change in horizon area while dQ and T are the energy flux across the horizon and Unruh temperature seen by an accelerating observer just inside the horizon. The internal entropy production term dS_i is proportional to the sq...

The black hole entropy formula applied to local Rindler horizon at each spacetime point has been used in the literature to derive the Einstein field equation as an equation of state of a thermodynamical system of spacetime. In the present paper we argue that due to the key role of causal structure and discrete spacetime in this approach the natural framework is unimodular relativity rather than general relativity. It is shown that the equation of state is trace free unimodula...

I argue that the field equations of any theory of gravity which is diffeomorphism invariant must be expressible as a thermodynamic identity, TdS=dE around any event in the spacetime. This fact can be demonstrated explicitly (and rather easily) if: (a) one accepts the Noether current of the theory as providing the definition for local entropy density and (b) one is allowed to introduce the local notions of a Rindler frame, acceleration horizon and a Killing vector (related to ...

It is possible to provide a physical interpretation for the field equations of gravity based on a thermodynamical perspective. The virtual degrees of freedom associated with the horizons perceived by the local Rindler observers, play a crucial role in this approach. In this context, the relation S=E/2T between the entropy (S), active gravitational mass (E) and temperature (T) - obtained previously in gr-qc/0308070 [CQG, 21, 4485 (2004)] - can be reinterpreted as the law of eq...

We show that the classical equations of gravity follow from a thermodynamic relation, dQ = T dS, where S is taken to be the Wald entropy, applied to a local Rindler horizon at any point in spacetime. Our approach works for all diffeomorphism-invariant theories of gravity. This suggests that classical gravity may be thermodynamic in origin.

We analyze spacetimes with horizons and study the thermodynamic aspects of causal horizons, suggesting that the resemblance between gravitational and thermodynamic systems has a deeper quantum mechanical origin. We find that the observer dependence of such horizons is a direct consequence of associating a temperature and entropy to a spacetime. The geometrical picture of a horizon acting as a one-way membrane for information flow can be accepted as a natural interpretation of...