Can a false vacuum bubble remove the singularity inside a black hole?

Suddhasattwa Brahma,Dong-Han Yeom

doi:10.1140/epjc/s10052-020-8248-4

Abstract

We investigate a regular black hole model with a de Sitter-like core at its center. This type of a black hole model with a false vacuum core was introduced with the hope of singularity-resolution and is a common feature shared by many regular black holes. In this paper, we examine this claim of a singularity-free black hole by employing the thin-shell formalism, and exploring its dynamics, within the Vaidya approximation. We find that during gravitational collapse, the shell necessarily moves along a space-like direction. More interestingly, during the evaporation phase, the shell and the outer apparent horizon approach each other but, unless the evaporation takes place very rapidly, the approaching tendency is too slow to avoid singularity-formation. This shows that albeit a false vacuum core may remove the singularity along the ingoing null direction, there still exists a singularity along the outgoing null direction, unless the evaporation is very strong.

Highlights

In the context of black holes, one is led to ask the natural question: which one of the assumptions of the singularity theorems [5] – (1) the existence of an apparent horizon, (2) global hyperbolicity, or (3) the null energy condition – is violated so as to bypass them? in order to understand exactly how a specific quantum gravity approach violates one of these three assumptions [6,7,8], we need to further assume that the quantum theory allows for an effective spacetime approach
In order to discuss some of the typical corrections which arise in the effective spacetime of regular black holes from the underlying quantum geometry, let us focus on the specific case of loop quantum gravity
In order to describe the transient region consistently, we need a model that can include field theoretical dynamics. (Such a field theoretical construction has largely been ignored in the literature far.) If the center is akin to de Sitter (dS) space, in principle, one can mimic the model with such a field theoretical structure

Summary

Introduction

The information loss paradox is one such problem which arises as a consequence of the classical singularity mentioned above. In order to understand this and other such problems, it is useful to investigate the dynamical causal structures of regular black hole models by studying the effective quantum gravitational completion of the evaporating spacetime [11,12]. For such black holes, the first condition – the existence of an apparent horizon – is necessary in order to. We correct some naive expectations of regular black hole models and point out overlooked issues in the typical causal structures of an evaporating regular black hole1 This lets us better formulate the following question: What is the genuine condition to obtain closed apparent horizons?. A major improvement of this type of a setup, when compared with similar dynamical regular black hole models, lies in its goal of connecting it to realistic evaporation scenarios

Metric ansatz

Field equations

Numerical solutions

Analysis: during evaporation

Conclusion

Internal structure