Surfaces away from horizons are not thermodynamic

TL;DR

This paper investigates whether non-horizon surfaces exhibit thermodynamic behavior similar to black hole horizons, finding that the first law of thermodynamics generally does not hold for such surfaces, challenging assumptions in emergent gravity theories.

Contribution

The paper provides a rigorous analysis showing the failure of the first law of thermodynamics for surfaces away from horizons, questioning their thermodynamic interpretation in emergent gravity.

Findings

First law holds on horizons in static asymptotically-flat spacetimes.

First law is a good approximation for stretched horizons.

Surfaces away from horizons generally do not satisfy the first law, except in symmetric cases.

Abstract

Since the 1970's it has been known that black hole (and other) horizons are truly thermodynamic in nature. More generally, surfaces which are not horizons have also been conjectured to behave thermodynamically. Initially, for surfaces microscopically expanded from a horizon to so-called stretched horizons, and more recently, for more general ordinary surfaces in the emergent gravity program. To test these conjectures we ask whether such surfaces satisfy an analogue to the first law of thermodynamics (as do horizons). For static asymptotically-flat spacetimes we find that such a first law holds on horizons. We rigorously prove that this law remains an excellent approximation for stretched horizons, but perhaps counter-intuitively this result illustrates the insufficiency of the laws of black hole mechanics alone from implying truly thermodynamic behavior. For surfaces away from horizons in the emergent gravity program the first law fails (with the exception of fully spherically symmetric scenarios) thus undermining the key thermodynamic assumption of this program.