< phi^2 > for a scalar field in 2D black holes: a new uniform approximation

Details < phi^2 > for a scalar field in 2D black holes: a new uniform approximation < phi^2 > for a scalar field in 2D black holes: a new uniform approximation

2002-12-10

arxiv.org/abs/hep-th/0212115v1

Phys.Rev. D67 (2003) 104003

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, 3 figures

Scientific paper

10.1103/PhysRevD.67.104003

We study nonconformal quantum scalar fields and averages of their local observables (such as ^{ren} and T_{ab}^{ren}) in a spacetime of a 2-dimensional black hole. In order to get an analytical approximation for these expressions the WKB approximation is often used. We demonstrate that at the horizon WKB approximation is violated for a nonconformal field, that is when the field mass or/and the parameter of non-minimal coupling do not vanish. We propose a new "uniform approximation" which solves this problem. We use this approximation to obtain an improved analytical approximation for ^{ren} in the 2-dimensional black hole geometry. We compare the obtained results with numerical calculations.

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