Matter Accretion Versus Semiclassical Bounce in Schwarzschild Interior

Kirill Bronnikov,Milena Skvortsova,Sergey Bolokhov

doi:10.3390/universe6100178

Kirill Bronnikov, Milena Skvortsova + Show 1 more

Open Access

https://doi.org/10.3390/universe6100178

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Journal: Universe	Publication Date: Oct 14, 2020
Citations: 4	License type: CC BY 4.0

Affiliation: Peoples' Friendship University of Russia

Abstract

We discuss the properties of the previously constructed model of a Schwarzschild black hole interior where the singularity is replaced by a regular bounce, ultimately leading to a white hole. We assume that the black hole is young enough so that the Hawking radiation may be neglected. The model is semiclassical in nature and uses as a source of gravity the effective stress-energy tensor (SET) corresponding to vacuum polarization of quantum fields, and the minimum spherical radius is a few orders of magnitude larger than the Planck length, so that the effects of quantum gravity should still be negligible. We estimate the other quantum contributions to the effective SET, caused by a nontrivial topology of spatial sections and particle production from vacuum due to a nonstationary gravitational field and show that these contributions are negligibly small as compared to the SET due to vacuum polarization. The same is shown for such classical phenomena as accretion of different kinds of matter to the black hole and its further motion to the would-be singularity. Thus, in a clear sense, our model of a semiclassical bounce instead of a Schwarzschild singularity is stable under both quantum and classical perturbations.

Highlights

The existence of singularities in various solutions of general relativity (GR) as well as many alternative classical theories of gravity, describing black holes or the early Universe, is an undesirable but apparently inevitable feature
The stress-energy tensor (SET) used to describe the vacuum polarization of quantum fields is taken in the form of of a linear combination of the tensors (1) Hμν and (2) Hμν obtained by variation of the curvature-quadratic invariants R2 and Rμν Rμν in the effective action in agreement with the renormalization methodology of quantum field theory in curved spacetimes [34,35]
The model is semiclassical in nature and is governed by vacuum polarization leading to the emergence of quadratic curvature invariants in the effective action

Summary

Introduction

The existence of singularities in various solutions of general relativity (GR) as well as many alternative classical theories of gravity, describing black holes or the early Universe, is an undesirable but apparently inevitable feature. Since matter can manifest its quantum properties at the atomic or macroscopic scales (as exemplified by lasers or the Casimir effect), one may hope that singularities in cosmology or black holes may be prevented at length scales much larger than the Planck one This would look more attractive both from the observational viewpoint and theoretically since the corresponding results, at least today, look more confident than those obtained with quantum gravity. The SET used to describe the vacuum polarization of quantum fields is taken in the form of of a linear combination of the tensors (1) Hμν and (2) Hμν obtained by variation of the curvature-quadratic invariants R2 and Rμν Rμν in the effective action in agreement with the renormalization methodology of quantum field theory in curved spacetimes [34,35] In this scenario, in the internal Kantowski–Sachs metric, the spherical radius r evolves to a regular minimum instead of zero, while its longitudinal scale has a regular maximum instead of infinity.

Near-Bounce Geometry

The Stress-Energy Tensor

The Semiclassical Bounce

Nonlocal Contribution to the Vacuum SET

CMB Accretion

Dust Accretion

Conclusions