Analytical approximation of the stress-energy tensor of a quantized scalar field in static spherically symmetric spacetimes

Abstract

Analytical approximations for 〈φ 2〉 and 〈T ν μ〉 of a quantized scalar field in static spherically symmetric spacetimes are obtained. The field is assumed to be both massive and massless, with an arbitrary coupling ξ to the scalar curvature, and in a zero temperature vacuum state. The expressions for 〈φ 2〉 and 〈T ν μ〉are divided into low- and high-frequency parts. The contributions of the high-frequency modes to these quantities are calculated for an arbitrary quantum state. As an example, the low-frequency contributions to 〈φ 2〉 and 〈T ν μ〉 are calculated in asymptotically flat spacetimes in a quantum state corresponding to the Minkowski vacuum (Boulware quantum state). The limits of the applicability of these approximations are discussed. © 2003 The American Physical Society.