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

Abstract

We study nonconformal quantum scalar fields and averages of their local observables (such as <phi^2>^{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 <phi^2>^{ren} in the 2-dimensional black hole geometry. We compare the obtained results with numerical calculations.

13 pages, 3 figures

References in corpus (6)

• Vacuum polarization in the Schwarzschild spacetime and dimensional reduction
• The Dimensional-Reduction Anomaly
• Non-Minimally Coupled Massive Scalar Field in a 2D Black Hole: Exactly Solvable Model
• Analitical approximation of $<{\varphi }^2>$ for a massive scalar field in static spherically symmetric spacetimes
• Vacuum Polarization of Massive Scalar Fields on the Black Hole Horizon
• Vacuum polarization of scalar fields near Reissner-Nordström black holes and the resonance behavior in field-mass dependence

Cited by in corpus (3)

• Extended Green-Liouville asymptotics and vacuum polarization for lukewarm black holes
• Analytical approximation for $<{\varphi }^2>$ of a quantized scalar field in ultrastatic asymptotically flat spacetimes
• Electrostatic self-energy and Bekenstein entropy bound in the massive Schwinger model