Noncommutative Black Hole Thermodynamics

Abstract

We give a general derivation, for any static spherically symmetric metric, of the relation $T_h=\frac{\mathcal{K}}{2\pi }$ connecting the black hole temperature ($T_h$) with the surface gravity ($\mathcal{K}$), following the tunneling interpretation of Hawking radiation. This derivation is valid even beyond the semi classical regime i. e. when quantum effects are not negligible. The formalism is then applied to a spherically symmetric, stationary noncommutative Schwarzschild space time. The effects of back reaction are also included. For such a black hole the Hawking temperature is computed in a closed form. A graphical analysis reveals interesting features regarding the variation of the Hawking temperature (including corrections due to noncommutativity and back reaction) with the small radius of the black hole. The entropy and tunneling rate valid for the leading order in the noncommutative parameter are calculated. We also show that the noncommutative Bekenstein-Hawking area law has the same functional form as the usual one.

LaTex, 17 pages, 2 figures, minor changes, references added, to appear in Phys. Rev. D

References in corpus (5)

• Corrections to Schwarzschild Solution in Noncommutative Gauge Theory of Gravity
• Hawking Radiation from General Kerr-(anti)de Sitter Black Holes
• Black Hole Thermodynamics and the Factor of 2 Problem
• Deformed Reissner--Nordstrom solutions in noncommutative gravity
• Hawking radiation as tunneling for spherically symmetric black holes: A generalized treatment

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• Corrected Entropy-Area Relation and Modified Friedmann Equations
• Hawking Radiation as Quantum Tunneling from Noncommutative Schwarzschild Black Hole
• Tunneling across dilaton-axion black holes
• Noncommutative Corrections to the Robertson-Walker metric
• Hawking Radiation from a Vaidya Black Hole: A Semi-Classical Approach and Beyond