A Local First Law of Gravity

Abstract

We find a (quasi-)local first law of thermodynamics, $\Delta E=T\Delta S-W$, connecting gravitational entropy, $S$, with matter energy and work. For Einstein gravity $S$ is the Bekenstein-Hawking entropy, while for general theories of gravity $S$ is the Wald entropy, evaluated on the stretched future light cone of any point in an arbitrary spacetime, not necessarily containing a black hole. The equation can be written as $\rho \Delta V=T\Delta S-p\Delta V$ by regarding the energy-momentum tensor as that of a fluid.

6 pages, 1 figure, LaTeX

References in corpus (4)

• Entanglement equilibrium for higher order gravity
• Unruh-DeWitt detector event rate for trajectories with time-dependent acceleration
• Einstein's Equations from the Stretched Future Light Cone
• Intrinsic and Extrinsic curvatures in Finsler-esque spaces

Cited by in corpus (4)

• Kinematics and dynamics of null hypersurfaces in the Einstein-Cartan spacetime and related thermodynamic interpretation
• Non-linear equation of motion for higher curvature semiclassical gravity
• Gravity from equilibrium thermodynamics of stretched light cones
• Thermal nature of a generic null surface