Regular black holes, universes without singularities, and phantom-scalar field transitions

TL;DR

This paper explores how non-singular cosmological models with scalar fields can lead to regular black holes and universe transitions, highlighting the role of scalar field potentials with cusp-like non-analyticities.

Contribution

It demonstrates a method to eliminate cosmological singularities, resulting in regular black holes and universe transitions using scalar fields with non-analytic potentials.

Findings

Transition between scalar and phantom scalar fields in non-singular cosmologies

Existence of singularity-free static spherically symmetric solutions

Reproduction of results in anisotropic Bianchi I universe

Abstract

We consider a procedure of elimination of cosmological singularities similar to that suggested in the recent paper by Simpson and Visser for the construction of regular black holes. It is shown that by imposing a non-singular cosmological evolution with a bounce in a flat Friedmann universe filled with a minimally coupled scalar field, we obtain a transition between the standard scalar field and its phantom counterpart. In this case, the potential of the scalar field has a non-analyticity of the cusp type. This result is also readily reproduced in the case of an anisotropic Bianchi I universe. We have also found a spherically symmetric static solution of the Einstein equations, free of singularities and sustained by a scalar field.