Effective Tolman temperature induced by trace anomaly

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 blueshift 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 there does not appear infinite blueshift of the Hawking temperature at the event horizon any more. In particular, it is vanishing on the horizon, so that the equivalence principle is exactly recovered at the horizon.

11 pages, 1 figure, version to appear in EPJC

References in corpus (5)

• Interior of Black Holes and Information Recovery
• Phenomenological Description of the Interior of the Schwarzschild Black Hole
• A Quantal Tolman Temperature
• Hawking versus Unruh effects, or the difficulty of slowly crossing a black hole horizon
• One-loop conformal anomaly in an implicit momentum space regularization framework

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• What Hawking Radiation Looks Like as You Fall into a Black Hole
• The effective Tolman temperature in curved spacetimes
• How the Schwarzschild-de Sitter horizons remain in thermal equilibrium at vastly different temperatures
• On thermal radiation of de Sitter space in the semiclassical Jackiw-Teitelboim model
• Hawking effect of AdS${}_2$ black hole in the Jackiw-Teitelboim model