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The Conical Singularity and Quantum Corrections to Entropy of Black Hole

Technical Report:

Abstract

It is well known that at the temperature different from the Hawking temperature there appears a conical singularity in the Euclidean classical solution of gravitational equations. The method of regularizing the cone by regular surface is used to determine the curvature tensors for such metrics. It allows to calculate the one-loop matter effective action and the corresponding one-loop quantum corrections to the entropy in the framework of the path integral approach of Gibbons and Hawking. The two-dimensional and four-dimensional cases are considered. The entropy of the Rindler space is shown to be divergent logarithmically in two dimensions and quadratically in four dimensions. It corresponds to the results obtained earlier. For the eternal 2D black hole we observe finite, dependent on the mass, correction to the entropy. The entropy of the 4D Schwarzschild black hole is shown to possess an additional (in comparison to the 4D Rindler space) logarithmically divergent correction which does not vanish in the limit of infinite mass of the black hole. We argue that infinities of the entropy in four dimensions are renormalized with the renormalization of the gravitational coupling. (author). 35 refs.
Authors:
Publication Date:
Dec 31, 1994
Product Type:
Technical Report
Report Number:
JINR-E-2-94-246
Reference Number:
SCA: 661000; PA: AIX-26:012149; EDB-95:031924; SN: 95001324629
Resource Relation:
Other Information: DN: Submitted to Physical Review. D, Particles Fields.; PBD: 1994
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; MATHEMATICAL SPACE; BLACK HOLES; QUANTUM FIELD THEORY; CONICAL CONFIGURATION; CORRECTIONS; MATHEMATICAL MANIFOLDS; SCHWARZSCHILD RADIUS; SINGULARITY; SPACE-TIME; 661000; GENERAL PHYSICS
OSTI ID:
10112347
Research Organizations:
Joint Inst. for Nuclear Research, Dubna (Russian Federation). Lab. of Theoretical Physics
Country of Origin:
JINR
Language:
English
Other Identifying Numbers:
Other: ON: DE95613367; TRN: XJ9406549012149
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
INIS
Size:
22 p.
Announcement Date:
Jun 30, 2005

Technical Report:

Citation Formats

Solodukhin, S N. The Conical Singularity and Quantum Corrections to Entropy of Black Hole. JINR: N. p., 1994. Web.
Solodukhin, S N. The Conical Singularity and Quantum Corrections to Entropy of Black Hole. JINR.
Solodukhin, S N. 1994. "The Conical Singularity and Quantum Corrections to Entropy of Black Hole." JINR.
@misc{etde_10112347,
title = {The Conical Singularity and Quantum Corrections to Entropy of Black Hole}
author = {Solodukhin, S N}
abstractNote = {It is well known that at the temperature different from the Hawking temperature there appears a conical singularity in the Euclidean classical solution of gravitational equations. The method of regularizing the cone by regular surface is used to determine the curvature tensors for such metrics. It allows to calculate the one-loop matter effective action and the corresponding one-loop quantum corrections to the entropy in the framework of the path integral approach of Gibbons and Hawking. The two-dimensional and four-dimensional cases are considered. The entropy of the Rindler space is shown to be divergent logarithmically in two dimensions and quadratically in four dimensions. It corresponds to the results obtained earlier. For the eternal 2D black hole we observe finite, dependent on the mass, correction to the entropy. The entropy of the 4D Schwarzschild black hole is shown to possess an additional (in comparison to the 4D Rindler space) logarithmically divergent correction which does not vanish in the limit of infinite mass of the black hole. We argue that infinities of the entropy in four dimensions are renormalized with the renormalization of the gravitational coupling. (author). 35 refs.}
place = {JINR}
year = {1994}
month = {Dec}
}