Schwarzschild geometry counterpart in semiclassical gravity

Abstract

We investigate the effects of vacuum polarization on vacuum static spherically-symmetric spacetimes. We start from the Polyakov approximation to the renormalized stress-energy tensor (RSET) of a minimally coupled massless scalar field. This RSET is not regular at $r=0$, so we define a regularized version of the Polyakov RSET. Using this Regularized RSET, and under the previous symmetry assumptions, we find all the solutions to the semiclassical field equations in vacuum. The resulting counterpart to the Schwarzschild classical geometry substitutes the presence of an event horizon by a wormhole throat that connects an external asymptotically flat region with an internal asymptotic region possessing a naked singularity: there are no semiclassical vacuum solutions with well-defined Cauchy surfaces. We also show that the Regularized Polyakov RSET allows for wormhole geometries of arbitrarily small throat radius. This analysis paves the way to future investigations of proper stellar configurations with an internal non-vacuum region.

arXiv comment22 pages, 4 figures, v2: references and minor changes added to match published version

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• Non-symmetric wormholes and localized Big Rip singularities in Einstein-Weyl gravity
• Islands in Non-Minimal Dilaton Gravity: Exploring Effective Theories for Black Hole Evaporation
• Asymptotically flat vacuum solutions in order-reduced semiclassical gravity
• Unveiling horizons in quantum critical collapse
• Vacuum semiclassical gravity does not leave space for safe singularities
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• Quantum Critical Collapse Abhors a Naked Singularity
• Dynamical evolution and stability of quantum corrected Schwarzschild black holes in semiclassical gravity
• Quantum corrected Einstein-Yang-Mills black holes in semiclassical gravity
• Stellar equilibrium on a physical vacuum soil
• Trace anomaly contributions to semi-classical wormhole geometries
• Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass
• Macroscopic backreaction of the trace anomaly on classical vacuum backgrounds
• Dynamical wormholes