Mimetic Black Holes

TL;DR

This paper explores static spherically symmetric solutions in mimetic gravity, revealing stealth black holes and singularities, and constructs a black hole model by matching exterior and interior solutions.

Contribution

It introduces a novel approach to modeling mimetic black holes by matching exterior static solutions with interior anisotropic spacetimes.

Findings

Existence of stealth Schwarzschild black holes with scalar hair.

Presence of naked singularities related to caustic formation.

Construction of a continuous mimetic black hole solution by matching exterior and interior spacetimes.

Abstract

In this paper, we look for the vacuum static spherically symmetric solution in the mimetic gravity scenario based on the conformal invariance principle. The trivial solution is a stealth Schwarzschild black hole with scalar hair where the mimetic field does not contribute to the background. However, a solution with two naked singularities shows up when the mimetic scalar field contributes to the background. We show that one of these singularities is the same as the singularity at the center of standard Schwarzschild black hole while the other appears due to caustics formation. However, we construct the mimetic black hole solution by gluing the exterior static spherically symmetric solution to a time-dependent anisotropic spacetime describing the interior of the black hole. It is shown that these two solutions match continuously on the surface of the apparent horizon. Some physical properties of the corresponding mimetic black holes are discussed.