Effective Tolman temperature induced by trace anomaly

• Main Authors: Myungseok Eune, Yongwan Gim, Wontae Kim
• Format: Article
• Language: English
• Published: SpringerOpen 2017-04-01
• Series: European Physical Journal C: Particles and Fields
• Subjects: Black Hole; Proper Temperature; Tangential Pressure; Symmetric Black Hole; Trace Anomaly
• Online Access: http://link.springer.com/article/10.1140/epjc/s10052-017-4812-y

Abstract Despite the finiteness of stress tensor for a scalar field on the four-dimensional Schwarzschild black hole in the Israel–Hartle–Hawking vacuum, the Tolman temperature in thermal equilibrium is certainly divergent on the horizon due to the infinite blue-shift of the Hawking temperature. The origin of this conflict is due to the fact that the conventional Tolman temperature was based on the assumption of a traceless stress tensor, which is, however, incompatible with the presence of the trace anomaly responsible for the Hawking radiation. Here, we present an effective Tolman temperature which is compatible with the presence of the trace anomaly by using the modified Stefan–Boltzmann law. Eventually, the effective Tolman temperature turns out to be finite everywhere outside the horizon, and so an infinite blue-shift of the Hawking temperature at the event horizon does not appear any more. In particular, it is vanishing on the horizon, so that the equivalence principle is exactly recovered at the horizon.