Thermodynamics of Horizons from a Dual Quantum System

• Main Authors: T. Padmanabhan, Sudipta Sarkar
• Format: Article
• Language: English
• Published: MDPI AG 2007-08-01
• Series: Entropy
• Subjects: Thermodynamics; Dual Quantum System
• Online Access: http://www.mdpi.com/1099-4300/9/3/100/

It was shown recently that, in the case of Schwarschild black hole, one can obtainthe 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 sphericallysymmetric horizon. We show that the idea works for a general case only if we define the en-tropy S as a congruence (“observerâ€Â) dependent quantity and the energy E as the integral overthe source of the gravitational acceleration for the congruence. In fact, in this case, one recov-ers the relation S = E/2T between entropy, energy and temperature previously proposed byone 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.