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

## TL;DR

This paper examines whether a false vacuum core in a black hole can prevent singularity formation, finding that it may only do so under rapid evaporation conditions, with singularities still likely to form.

## Contribution

It provides a detailed analysis of the dynamics of false vacuum core black holes using thin-shell formalism and Vaidya approximation, highlighting limitations in singularity resolution.

## Key findings

- False vacuum core may remove ingoing null singularity
- Singularity persists along outgoing null direction unless evaporation is rapid
- Shell dynamics are necessarily spacelike during collapse

## 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.