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Thermodynamics of Horizons from a Dual Quantum System
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Received: 10 July 2007; Accepted: 13 August 2007 / Published: 20 August 2007
Abstract: 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 (“observer”) 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.
Keywords: Thermodynamics; Dual Quantum System
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Sarkar, S.; Padmanabhan, T. Thermodynamics of Horizons from a Dual Quantum System. Entropy 2007, 9, 100-107.
Sarkar S, Padmanabhan T. Thermodynamics of Horizons from a Dual Quantum System. Entropy. 2007; 9(3):100-107.
Sarkar, Sudipta; Padmanabhan, T. 2007. "Thermodynamics of Horizons from a Dual Quantum System." Entropy 9, no. 3: 100-107.