Asymptotically flat vacuum solutions in order-reduced semiclassical gravity

TL;DR

This paper develops a new analytic approximation for the renormalized stress-energy tensor in semiclassical gravity, enabling the classification of asymptotically flat vacuum solutions in the context of quantum backreaction on Schwarzschild spacetime.

Contribution

It introduces a novel order-reduction method for the AHS approximation, producing well-posed semiclassical equations and classifying their solutions.

Findings

Derived a new analytic RSET approximation with desired properties.

Classified self-consistent semiclassical solutions in Boulware state.

Compared solutions with previous Polyakov approximation results.

Abstract

We investigate the effects of quantum backreaction on the Schwarzschild geometry in the semiclassical approximation. The renormalized stress-energy tensor (RSET) of a scalar field is modelled via an order reduction of the analytical approximation derived by Anderson, Hiscock and Samuel (AHS). As the resulting AHS semiclassical Einstein equations are of fourth-derivative order in the metric, we follow a reduction of order prescription to shrink the space of solutions. Motivated by this prescription, we develop a method that allows to obtain a novel analytic approximation for the RSET that exhibits all the desired properties for a well-posed RSET: conservation, regularity, and correct estimation of vacuum-state contributions. We derive a set of semiclassical equations sourced by the order-reduced AHS-RSET in the Boulware state. We classify the self-consistent solutions to this set of field equations, discuss their main features and address how well they resemble the solutions of the higher-order semiclassical theory. Finally, we establish a comparison with previous results in the literature obtained through the Polyakov approximation for minimally coupled scalar fields.