Noncommutative black hole thermodynamics

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 backreaction 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 backreaction) 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.