Entropy corrections for Schwarzschild and Reissner--Nordstrom black holes

doi:10.1088/0264-9381/21/6/007

Entropy corrections for Schwarzschild and Reissner–Nordström black holes

M M Akbar et al 2004 Class. Quantum Grav. 21 1383-1392 doi: 10.1088/0264-9381/21/6/007

PDF (117 KB) | References | Articles citing this article

M M Akbar¹ and Saurya Das^2,3
¹ Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
² Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick E3B 5A3, Canada
³ Present address: Department of Physics, University of Lethbridge, 4401 University Drive, Lethbridge, Alberta T1K 3M4, Canada
E-mail: M.M.Akbar@damtp.cam.ac.uk and saurya.das@uleth.ca

Abstract. A Schwarzschild black hole being thermodynamically unstable, corrections to its entropy due to small thermal fluctuations cannot be computed. However, a thermodynamically stable Schwarzschild solution can be obtained within a cavity of any finite radius by immersing it in an isothermal bath. For these boundary conditions, classically there are either two black-hole solutions or no solution. In the former case, the larger mass solution has a positive specific heat and hence is locally thermodynamically stable. We find that the entropy of this black hole, including first-order fluctuation corrections, is given by: ${\cal S} = S_{BH} - \ln\big[\frac{3}{R} (S_{BH}/4{\pi})^{1/2} -2\big]^{-1} + \case{1}{2} \ln(4{\pi})$ , where S_BH = A/4 is its Bekenstein–Hawking entropy and R is the radius of the cavity. We extend our results to four-dimensional Reissner–Nordström black holes, for which the corresponding expression is: ${\cal S} = S_{BH} - \frac{1}{2} \ln [(S_{BH}/ {\pi} R^2) \big({3S_{BH}}/ {{\pi} R^2} - 2\sqrt{{S_{BH}}/{{\pi} R^2 - {\alpha}^2}}\big)$ $\big(\sqrt{{S_{BH}}/{{\pi} R^2}} - {\alpha}^2\big)\big/ ({S_{BH}}/ {{\pi} R^2} -{\alpha}^2)^2 ]^{-1} +\case{1}{2} \ln(4{\pi})$ . Finally, we generalize the stability analysis to Reissner–Nordström black holes in arbitrary spacetime dimensions, and compute their leading order entropy corrections. In contrast to previously studied examples, we find that the entropy corrections in these cases have a different character.

PACS numbers: 04.60.−m, 04.70.−s, 04.70.Dy

Print publication: Issue 6 (21 March 2004)
Received 11 November 2003
Published 20 February 2004

Post to CiteUlike |

Post to Connotea |

Post to Bibsonomy

Entropy corrections for Schwarzschild and Reissner–Nordström black holes

Find related articles

Article options

Authors & Referees