Can a false vacuum bubble remove the singularity inside a black hole?
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Regular Article - Theoretical Physics
Can a false vacuum bubble remove the singularity inside a black hole? Suddhasattwa Brahma1,2,a , Dong-han Yeom3,4,b 1
Asia Pacific Center for Theoretical Physics, Pohang 37673, Republic of Korea Department of Physics, McGill University, Montréal, QC H3A 2T8, Canada 3 Department of Physics Education, Pusan National University, Busan 46241, Republic of Korea 4 Research Center for Dielectric and Advanced Matter Physics, Pusan National University, Busan 46241, Republic of Korea
2
Received: 23 September 2019 / Accepted: 15 July 2020 © The Author(s) 2020
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.
1 Introduction One of the most challenging problems in fundamental physics remains the appearance of classical singularities within the cores of black holes [1]. Singularity theorems in general relativity (GR) [2] generically leads to such regions where the classical notions of spacetime stop being meaningful. The general consensus is that, near Planckian curvatures, a theory of quantum gravity should supersede classical GR thereby resolving the singularity. For instance, in a vast array of quantum cosmological models [3,4], one finds that the curvature invariants reach a maximum, without blowing up to infinity, due to the appearance of quantum gravity cora e-mail:
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b e-mail:
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rections. In the context of black holes, one is then 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? However, in order to understand exactly how a specific quantum gravity approach violates one of these three assumptions [6–8], we need to further assume that the quantum theory allows for an effective spacetime approach. This can be understood as follows: It is entirely possible that singularity-resolution is a completely ‘quantum’ process which requires solving the Wheeler deWitt equation [9], or some regulariz
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