Abstract:
We find a local first law of thermodynamics, ΔE=TΔS−W, connecting gravitational entropy, S, with matter energy and work. For Einstein gravity S is the Bekenstein-Hawking entropy, while for more 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 also be written as ρΔV=TΔS−pΔV by regarding the energy-momentum tensor as that of a fluid.