Komar energy and Smarr formula for noncommutative Schwarzschild black hole

Banerjee, Rabin; Gangopadhyay, Sunandan

doi:10.1007/s10714-011-1250-2

Komar energy and Smarr formula for noncommutative Schwarzschild black hole

2011

5 pages

Published in:

Gen.Rel.Grav. 43 (2011) 3201

e-Print:

1008.1683 [hep-th]

DOI:

10.1007/s10714-011-1250-2

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Abstract: (arXiv)

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.

Note:

5 pages Latex

11.10.Nx
Komar energy
Noncommutative blackhole
black hole: Schwarzschild
higher-order: 0
higher-order: 1
black hole: noncommutative
black hole: thermodynamics
deformation
black hole: energy

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