Noncommutative Black Hole Thermodynamics

TL;DR

This paper derives a generalized relation between black hole temperature and surface gravity applicable beyond semi-classical limits, applies it to noncommutative Schwarzschild black holes, and analyzes how noncommutativity and back reaction affect thermodynamic properties.

Contribution

It provides a universal derivation of black hole temperature from tunneling, extends the analysis to noncommutative geometries, and includes back reaction effects in the thermodynamics.

Findings

Closed-form Hawking temperature for noncommutative black holes.

Noncommutative corrections preserve the Bekenstein-Hawking area law.

Graphical analysis shows temperature variations with black hole radius.

Abstract

We give a general derivation, for any static spherically symmetric metric, of the relation $T_h=\frac{\cal K}{2\pi}$ connecting the black hole temperature ($T_h$) with the surface gravity ($\cal K$), 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.