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Register a new userAnomalies, effective action and Hawking temperatures of a Schwarzschild black hole in the isotropic coordinates
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Motivated by the universality of Hawking radiation and that of the anomaly cancellation technique as well as that of the effective action method, we investigate the Hawking radiation of a Schwarzschild black hole in the isotropic coordinates via the cancellation of gravitational anomaly. After performing a dimensional reduction from the four-dimensional isotropic Schwarzschild metric, we show that this reduction procedure will, in general, result in two classes of two-dimensional effective metrics: the conformal equivalent and the inequivalent ones. For the physically equivalent class, the two-dimensional effective metric displays such a distinct feature that the determinant is not equal to the unity ($sqrt{-g} eq 1$), but also vanishes at the horizon, the latter of which possibly invalidates the anomaly analysis there. ... This is an updated version to replace our e-print arXiv:0709.0044 [hep-th]. Abstract is too long to exceed the limit of 24 lines by arXiv.
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This paper has been withdrawn by the authors due to an incorrect statement on the viability of the Robinson-Wilczek method when applied to the case when the metric determinant vanishes at the horizon. This paper has been replaced by arXiv:0803.1338 [hep-th].
We extend the work by S. Iso, H. Umetsu and F. Wilczek [Phys. Rev. Lett. 96 (2006) 151302] to derive the Hawking flux via gauge and gravitational anomalies of a most general two-dimensional non-extremal black hole space-time with the determinant of its diagonal metric differing from the unity ($sqrt{-g} eq 1$) and use it to investigate Hawking radiation from the Reissner-Nordstrom black hole with a global monopole by requiring the cancellation of anomalies at the horizon. It is shown that the compensating energy momentum and gauge fluxes required to cancel gravitational and gauge anomalies at the horizon are precisely equivalent to the $(1+1)$-dimensional thermal fluxes associated with Hawking radiation emanating from the horizon at the Hawking temperature. These fluxes are universally determined by the value of anomalies at the horizon.
Hawking flux from the Schwarzschild black hole with a global monopole is obtained by using Robinson and Wilczeks method. Adopting a dimension reduction technique, the effective quantum field in the (3+1)--dimensional global monopole background can be described by an infinite collection of the (1+1)--dimensional massless fields if neglecting the ingoing modes near the horizon, where the gravitational anomaly can be cancelled by the (1+1)--dimensional black body radiation at the Hawking temperature.
Former part of this article is the proceedings for my talk on 2004.07474, which is a report on the issue in the title of this article. Later part is the detailed description of 2004.07474.
The anomaly cancelation method proposed by Wilczek et al. is applied to the black holes of topologically massive gravity (TMG) and topologically massive gravito-electrodynamics (TMGE). Thus the Hawking temperature and fluxes of the ACL and ACGL black holes are found. The Hawking temperatures obtained agree with the surface gravity formula. Both black holes are rotating and this gives rise to appropriate terms in the effective U(1) gauge field of the reduced (1+1)-dimensional theory. It is found that the terms in this U(1) gauge field correspond exactly to the correct angular velocities on the horizon of both black holes as well as the correct electrostatic potential of the ACGL black hole. So the results for the Hawking fluxes derived here from the anomaly cancelation method, are in complete agreement with the ones obtained from integrating the Planck distribution.
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