Komar energy and Smarr formula for noncommutative inspired Schwarzschild black hole |
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Authors: | Rabin Banerjee Sunandan Gangopadhyay |
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Affiliation: | (1) S.N. Bose National Centre for Basic Sciences, JD Block, Sector III, Salt Lake, Kolkata, 700098, India;(2) Narasinha Dutt College, 129, Belilious Road, Howrah, 711101, India |
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Abstract: | We calculate the Komar energy E for a noncommutative inspired 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 θ (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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