Thermodynamics of horizons from a dual quantum system

TL;DR

This paper extends a dual quantum system approach to derive thermodynamic relations for general spherically symmetric horizons, revealing observer-dependent entropy and quantum corrections to entropy formulas.

Contribution

It generalizes the dual quantum system method to all spherically symmetric horizons, defining entropy as observer-dependent and calculating quantum corrections.

Findings

Validates the duality approach for general horizons

Defines entropy as observer-dependent quantity

Calculates quantum corrections to Bekenstein-Hawking entropy

Abstract

It was shown recently that, in the case of Schwarschild black hole, one can obtain the correct thermodynamic relations by studying a model quantum system and using a particular duality transformation. We study this approach further for the case a general spherically symmetric horizon. We show that the idea works for a general case only if we define the entropy S as a congruence ("observer") dependent quantity and the energy E as the integral over the source of the gravitational acceleration for the congruence. In fact, in this case, one recovers the relation S=E/2T between entropy, energy and temperature previously proposed by one of us in gr-qc/0308070. This approach also enables us to calculate the quantum corrections of the Bekenstein-Hawking entropy formula for all spherically symmetric horizons.