Black Hole Thermodynamics From Near-horizon Conformal Quantum Mechanics

Black hole thermodynamics from near-horizon conformal quantum mechanics

Horacio E. Camblong1 and Carlos R. Ordo´n˜ez2,3 1 Department of Physics, University of San Francisco, San Francisco, California 94117-1080, USA 2 Department of Physics, University of Houston, Houston, Texas 77204-5506, USA 3 World Laboratory Center for Pan-American Collaboration in Science and Technology, University of Houston Center, Houston, Texas 77204-5506, USA (Received 27 December 2004; revised manuscript received 31 March 2005; published 23 May 2005) 

The thermodynamics of black holes is shown to be directly induced by their near-horizon conformal invariance. This behavior is exhibited using a scalar field as a probe of the black hole gravitational background, for a general class of metrics in D spacetime dimensions (with D 4). The ensuing analysis is based on conformal quantum mechanics, within a hierarchical near-horizon expansion. In particular, the leading conformal behavior provides the correct quantum statistical properties for the BekensteinHawking entropy, with the near-horizon physics governing the thermodynamics from the outset. Most importantly: (i) this treatment reveals the emergence of holographic properties; (ii) the conformal coupling parameter is shown to be related to the Hawking temperature; and (iii) Schwarzschild-like coordinates, despite their ‘‘coordinate singularity,’’ can be used self-consistently to describe the thermodynamics of black holes. DOI: 10.1103/PhysRevD.71.104029

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