THERMODYNAMICS OF SPACETIME - THE EINSTEIN EQUATION OF STATE

The Einstein equation is derived from the proportionality of entropy a nd the horizon area together with the fundamental relation delta Q = T dS. The key idea is to demand that this relation hold for all the loc al Rindler causal horizons through each spacetime point, with delta Q and T interpreted as the energy flux and Unruh temperature seen by an accelerated observer just inside the horizon. This requires that gravi tational lensing by matter energy distorts the causal structure of spa cetime so that the Einstein equation holds. Viewed in this way, the Ei nstein equation is an equation of state.