Asymptotically flat vacuum solutions in order-reduced semiclassical gravity

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.

20 pages, 4 figures. v2: Added minor comments and corrected typos to match published version

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• Quantum corrected Einstein-Yang-Mills black holes in semiclassical gravity
• Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass
• Stellar equilibrium on a physical vacuum soil
• Macroscopic backreaction of the trace anomaly on classical vacuum backgrounds