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On One-loop Quantum Corrections to the Thermodynamics of Charged Black Holes | | V.P.Frolov
; W. Israel
; S.N.Solodukhin
; | | Date: |
19 Feb 1996 | | Journal: | Phys.Rev. D54 (1996) 2732-2745 | | Subject: | hep-th gr-qc | | Abstract: | Quantum corrections are studied for a charged black hole in a two-dimensional model obtained by spherisymmetric reduction of the 4D Einstein-Maxwell theory. The classical (tree-level) thermodynamics is re-formulated in the framework of the off-shell approach, considering systems at arbitrary temperature. This implies a conical singularity at the horizon and modifies the gravitational action by terms defined on the horizon. A consistent variational procedure for the action functional is formulated. It is shown that the free energy reaches an extremum on the regular manifold with $T=T_H$. The one-loop contribution to the action in the Liouville-Polyakov form is re-examined. All the boundary terms are taken into account and the dependence on the state of the quantum field is established. The modification of the Liouville-Polyakov term for a 2D space with a conical defect is derived. The backreaction of the Hawking radiation on the geometry is studied and the quantum-corrected black hole metric is calculated perturbatively. Within the off-shell approach the one-loop thermodynamical quantities, energy and entropy, are found. They are shown to contain a part due to hot gas surrounding he black hole and a part due to the hole itself. It is noted that the contribution of the hot gas can be eliminated by appropriate choice of the (generally, non-flat) reference geometry. The deviation of the {it `` entropy - horizon area’’} relation for the quantum-corrected black hole from the classical law is discovered and possible physical consequences are discussed. | | Source: | arXiv, hep-th/9602105 | | Services: | Forum | Review | PDF | Favorites | |
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