Thermodynamics of Spacetime: The Einstein Equation of State

A general ansatz for gravitational entropy can be provided using the criterion that, any patch of area which acts as a horizon for a suitably defined accelerated observer, must have an entropy proportional to its area. After providing a brief justification for this ansatz, several consequences are derived: (i) In any static spacetime with a horizon and associated temperature $\beta^{-1}$, this entropy satisfies the relation $S=(1/2)\beta E$ where $E$ is the energy source for ...

For Rindler observers accelerating close to the horizon in local patches around a spacetime point, the matter-energy passing through the horizon increases the entropy and heat energy. Jacobson has showed that the Einstein equation can be derived from the consideration of this thermodynamic process. This, however, works only if the acceleration $a$ is much larger than the scale set by the curvature of the spacetime. It is explored here whether an extension is possible to the c...

I describe the conceptual and mathematical basis of an approach which describes gravity as an emergent phenomenon. Combining principle of equivalence and principle of general covariance with known properties of local Rindler horizons, perceived by observers accelerated with respect to local inertial frames, one can prove that the field equations describing gravity in any diffeomorphism invariant theory can be given a thermodynamic re-interpretation. This fact, in turn, leads ...

One of the striking features of general relativity is that the Einstein equation is implied by the Clausius relation imposed on a small patch of locally constructed causal horizon. Extension of this thermodynamic derivation of the field equation to more general theories of gravity has been attempted many times in the last two decades. In particular, equations of motion for minimally coupled higher curvature theories of gravity, but without the derivatives of curvature, have p...

A possible way to capture the effects of quantum gravity in spacetime at a mesoscopic scale, for relatively low energies, is through an energy dependent metric, such that particles with different energies probe different spacetimes. In this context, a clear connection between a geometrical approach and modifications of the special relativistic kinematics has been shown in the last few years. In this work, we focus on the geometrical interpretation of the relativistic deformed...

The fact that a temperature and an entropy may be associated with horizons in semi-classical general relativity has led many to suspect that spacetime has microstructure. If this is indeed the case then its description via Riemannian geometry must be regarded as an effective theory of the aggregate behavior of some more fundamental degrees of freedom that remain unknown, in many ways similar to the treatment of fluid dynamics via the Navier-Stokes equations. This led us to as...

The Einstein-Hilbert action (and thus the dynamics of gravity) can be obtained by combining the principle of equivalence, special relativity and quantum theory in the Rindler frame and postulating that the horizon area must be proportional to the entropy. This approach uses the local Rindler frame as a natural extension of the local inertial frame, and leads to the interpretation that the gravitational action represents the free energy of the spacetime geometry. As an aside, ...

It is suggested that the Einstein equation can be derived from Landauer's principle applied to an information erasing process at a local Rindler horizon and Jacobson's idea linking the Einstein equation with thermodynamics. When matter crosses the horizon, the information of the matter disappears and the horizon entanglement entropy increases to compensate the entropy reduction. The Einstein equation describes an information-energy relation during this process, which implies ...

I show that the gravitational dynamics in a bulk region of space can be connected to a thermodynamic description in the boundary of that region, thereby providing clear physical interpretations of several mathematical features of classical general relativity: (1) The Noether charge contained in a bulk region, associated with a specific time evolution vector field, has a direct thermodynamic interpretation as the gravitational heat content of the boundary surface. (2) This res...

Expanding the black hole thermodynamics from the horizon to achronal Cauchy hypersurface, the general relation between the Einstein equation and thermodynamics is established. Starting from trivial entropy that is generalized by Bekenstein-Hawking entropy, the entropic mass of matter emerges naturally together with Unruh temperature. The key idea is that the cause of mass formation comes down to trivial entropy, and mass density is just the external manifestation of mass. The...