Thermodynamics of spacetime from minimal area

TL;DR

This paper derives Hawking temperature and Bekenstein entropy from a minimal area concept, introduces quantum gravity corrections, and links minimal area to black hole and causal diamond thermodynamics.

Contribution

It provides a heuristic derivation of black hole thermodynamics from minimal area and explores quantum gravity corrections consistent with other approaches.

Findings

Quantum gravity corrections match other methods' results.

Minimal area constrained by black hole entropy content.

New relation between Unruh temperature and causal diamond entropy.

Abstract

Motivated by exploring the interface between thermodynamics of spacetime and quantum gravity effects, we develop a heuristic derivation of Hawking temperature and Bekenstein entropy from the existence of a minimal resolvable area. Moreover, we find leading order quantum gravity corrections to them that are in qualitative agreement with results obtained by other methods, both heuristic and rigorous. In this way, we recover, as a particular case, the corrections heuristically obtained from the existence of minimal length. We also show that the size of minimal area is constrained from above by well understood results of semiclassical black hole physics, specifically by the entropy content of Hawking radiation. The minimal area derivation we introduce is also applied to finding the Unruh temperature associated with causal diamonds and to establish a new relation between this temperature and the entropy of the causal diamond's horizon.