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.

arXiv comment20 pages, 4 figures. v2: Added minor comments and corrected typos to match published version

References in corpus (31)

• Testing the nature of dark compact objects: a status report
• The fuzzball proposal for black holes: an elementary review
• Everything You Always Wanted To Know About The Cosmological Constant Problem (But Were Afraid To Ask)
• Echoes from the Abyss: Tentative evidence for Planck-scale structure at black hole horizons
• Does backreaction enforce the averaged null energy condition in semiclassical gravity?
• Quantum Transfiguration of Kruskal Black Holes
• Is Quantum Gravity Necessary?
• Einstein Equation with Quantum Corrections Reduced to Second Order
• Phenomenological aspects of black holes beyond general relativity
• Self-consistent Wormhole Solutions of Semiclassical Gravity
• Gravitational vacuum polarization II: Energy conditions in the Boulware vacuum
• The Internal Geometry of an Evaporating Black Hole
• Versatile method for renormalized stress-energy computation in black-hole spacetimes
• Singularities and Quantum Gravity
• Stellar equilibrium in semiclassical gravity
• Where does the physics of extreme gravitational collapse reside?
• The quantum fate of black hole horizons
• Classical mass inflation vs semiclassical inner horizon inflation
• A quantum peek inside the black hole event horizon
• Static Black Holes With Back Reaction From Vacuum Energy
• Quantum fluxes at the inner horizon of a spinning black hole
• Schwarzschild geometry counterpart in semiclassical gravity
• Semiclassical constant-density spheres in a regularized Polyakov approximation
• Semiclassical relativistic stars
• Hadamard Renormalization of the Stress Energy Tensor in a Spherically Symmetric Black Hole Space-Time with an Application to Lukewarm Black Holes
• Reissner-Nordström geometry counterpart in semiclassical gravity
• Generalized Virasoro anomaly and stress tensor for dilaton coupled theories
• Perturbative reduction of derivative order in EFT
• Analytical approximation of the stress-energy tensor of a quantized scalar field in static spherically symmetric spacetimes
• The Schwarzschild singularity: a semiclassical bounce?
• Order reduction in semiclassical cosmology

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• Singularity resolution in spherically reduced 2D semiclassical gravity with negative central charge
• 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