Analytical approximation for⟨φ2⟩of a quantized scalar field in ultrastatic asymptotically flat spacetimes

Abstract

Analytical approximations for h' 2 i 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 to the scalar curvature, and in a zero or nonzero temperature vacuum state. The expression for h' 2 i 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 h' 2 i 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.

Stress tensor from the trace anomaly in Reissner-Nordström spacetimes

“…Several approaches to approximating T a b have been discussed previously in the literature, developed with important special cases in mind, such as static geometries with a timelike Killing field [16,19,20,21,22,23,24,25]. These approximations are quite successful for regular states in the Schwarzschild geometry, but fail when compared to the numerical results for T a b in the charged RN spacetimes.…”