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Black Hole Thermodynamics from Near-Horizon Conformal Quantum Mechanics

Horacio E. Camblong·Carlos R. Ordonez
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Abstract

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 $D \geq 4$). 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 Bekenstein-Hawking entropy, with the near-horizon physics governing the thermodynamic properties 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.

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Horacio E. Camblong, Carlos R. Ordonez. 2005-06-09. Black Hole Thermodynamics from Near-Horizon Conformal Quantum Mechanics. https://doi.org/10.1103/physrevd.71.104029

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