科研之友
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摘要
Motivated by the universality of Hawking radiation and that of the anomaly cancellation technique as well as 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 (root-g not equal 1)but also vanishes at the horizon, the latter of which possibly invalidates the anomaly analysis there. Nevertheless, in this paper we adopt the effective action method to prove that the consistent energy-momentum tensor T(t)(r) is divergent on the horizon but root-gT(t)(r) remains finite there. Meanwhile, through an explicit calculation we show that the covariant energy-momentum tensor T(t)(r) equals zero at the horizon. Therefore the validity of the covariant regularity condition that demands T(t)(r) =0 at the horizon has been justified, indicating that the gravitational anomaly analysis can be safely extrapolated to the case where the metric determinant vanishes at the horizon. It is then demonstrated that for the physically equivalent reduced metric, both methods can give the correct Hawking temperature of the isotropic Schwarzschild black hole, while for the inequivalent one with with determinant root-g=1 it can only give half of the correct temperature. We further exclude the latter undesired result by taking into account the general covariance of the energy-momentum tensor under the isotropic coordinate transformation.
- 出版日期2008-7-7
- 单位华中师范大学
