Analytical approximation for $<{\varphi }^2>$ of a quantized scalar field in ultrastatic asymptotically flat spacetimes

Abstract

Analytical approximations for $<{\varphi }^2>$ of a quantized scalar field in ultrastatic asymptotically flat spacetimes are obtained. The field is assumed to be both massive and massless, with an arbitrary coupling $\xi$ to the scalar curvature, and in a zero or nonzero temperature vacuum state. The expression for $<{\varphi }^2>$ is divided into low- and high-frequency parts. The expansion for the high-frequency contribution to this quantity is obtained. This expansion is analogous to the DeWitt-Schwinger one. As an example, the low-frequency contribution to $<{\varphi }^2>$ is calculated on the background of the small perturbed flat spacetime in a quantum state corresponding to the Minkowski vacuum at the asymptotic. The limits of the applicability of these approximations are discussed.

revtex4, 9 pages

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Cited by in corpus (5)

• Stress Tensor from the Trace Anomaly in Reissner-Nordstrom Spacetimes
• Vacuum polarization for lukewarm black holes
• Vacuum Polarization Effects on Flat Branes due to a Global Monopole
• Vacuum polarization of the quantized massive scalar field in the global monopole spacetime II: the renormalized quantum stress energy tensor
• Vacuum polarization of the quantized massive scalar field in the global monopole spacetime I: the field fluctuation