Hawking radiation and conformal anomalies in two-dimensional AdS spacetimes

Abstract

The Hawking radiation is one of most interesting known effects of black hole physics. Since its discovery in 1974 by Hawking, this phenomenon has been an object of study of great interest. Despite the large number of works on this subject, details of the quantum evolution of black holes are still unknown. In large part, this is due to the complexity of the calculations necessary to get such results. In order to calculate the Hawking radiation, but avoiding mathematical complications, many years ago Christensen and Fulling had proposed a method to derive the Hawking radiation flux in terms of trace anomalies, which is a very simple way to obtain consistent results, since the anomaly is given in terms of the spacetime curvature invariants. This approach is successful in the calculation of the stress tensor of the Hawking radiation emitted by black holes in two-dimensional spacetimes, where all the nonzero components of the stress tensor can be obtained. However, in the case of four-dimensional spacetimes the Christensen-Fulling method does not furnish a complete result, since the transverse components of the stress tensor cannot be determined. In this work we review such an approach and apply it to two-dimensional static black holes in asymptotically Minkowski and anti-de Sitter (AdS) spacetimes. For black holes in asymptotically AdS spacetimes a straightforward application of the Christensen-Fulling method does not provide correct results. To overcome this problem, we propose a slight modification of the method, where we argue that the trace anomaly due the background curvature of the AdS spacetime, without the black hole, should be deducted from the total trace anomaly, and hence we get the correct results for the energy flux of the Hawking radiation in all AdS spacetimes we have tested.