Komar energy and Smarr formula for noncommutative Schwarzschild black hole

Details Komar energy and Smarr formula for noncommutative Schwarzschild black hole Komar energy and Smarr formula for noncommutative Schwarzschild black hole

2010-08-10

arxiv.org/abs/1008.1683v1

Gen. Rel. Grav. 43, (2011) 3201-3212

Physics

High Energy Physics

High Energy Physics - Theory

5 pages Latex

Scientific paper

We calculate the Komar energy $E$ for a noncommutative Schwarzschild black hole. A deformation from the conventional identity $E=2ST_H$ is found in the next to leading order computation in the noncommutative parameter $\theta$ (i.e. $\mathcal{O}(\sqrt{\theta}e^{-M^2/\theta})$) which is also consistent with the fact that the area law now breaks down. This deformation yields a nonvanishing Komar energy at the extremal point $T_{H}=0$ of these black holes. We then work out the Smarr formula, clearly elaborating the differences from the standard result $M=2ST_H$, where the mass ($M$) of the black hole is identified with the asymptotic limit of the Komar energy. Similar conclusions are also shown to hold for a deSitter--Schwarzschild geometry.

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