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| Paper IPM / P / 6591 |
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| Abstract: | |||||
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The Hadamard renormalization prescription is used to derive a two-dimensional
analog of the renormalized stress tensor for a minimally coupled scalar field
in Schwarzschild-de Sitter space-time. In the two-dimensional analog the
minimal coupling reduces to the conformal coupling and the stress tensor is
found to be determined by the (nonlocal) contribution of the anomalous trace
and some additional parameters in close relation to the work by Christensen and
Fulling. To properly relate the stress tensor to
the state of outwards signals coming from the direction of the black hole at
late times we propose a cutoff hypothesis that excludes the contribution of the
anomalous trace close to the black hole horizon. The corresponding cutoff scale
is found to be related to the equilibrium temperature of the cosmological
horizon in a leading order estimate. Finally, we establish a relation between
the radiation temperature of the black hole horizen at large distance from the
hole and the anomalous trace and determine
the correction term to the Hawking temperature due to the presence of the
cosmological horizon.
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