Thermodynamics of horizons from a dual quantum system

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 partic-ular 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 en-tropy 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 recov-ers the relation S = E = 2 T between entropy, energy and temperature previously proposed by one of us in gr-qc/0308070. This approach also enables us to calculate the quantum correc-tions of the Bekenstein-Hawking entropy formula for all spherically symmetric horizons.