Tunneling/WKB and anomaly methods for Rindler and de sitter space-times

Abstract

We consider the WKB/tunneling method explicitly in the context of its application to the Rindler and de Sitter space-times. We also present two gravitational anomaly methods (consistent and covariant). The anomaly methods applied to the Rindler space-time do not reproduce the expected Unruh radiation, because the Rindler space-time does not have an anomaly. The consistent and the covariant anomaly methods give different results for the de Sitter space-time. In contrast to them, the WKB/tunneling method is a semiclassical calculation in which the radiation is regarded as a tunneling of quantum fields across the horizon. The tunneling method is applicable in all the indicated cases. But to recover the correct Gibbons-Hawking temperature, a previously overlooked temporal piece that contributes to the total action must be taken into account.