Black hole solutions in mimetic Born-Infeld gravity

TL;DR

This paper explores black hole solutions in mimetic Born-Infeld gravity, revealing how the mimetic field modifies singularity structures and affects the infall time of observers, offering new insights into black hole physics.

Contribution

It introduces and analyzes vacuum black hole solutions in mimetic Born-Infeld gravity, highlighting modifications to singularity nature due to the mimetic field.

Findings

Singularity inside Schwarzschild black holes can become lightlike due to the mimetic field.

The curvature invariants still diverge at the singularity.

The proper time for infalling observers to reach the singularity can be infinite.

Abstract

The vacuum, static, and spherically symmetric solutions in the mimetic Born-Infeld gravity are studied. The mimetic Born-Infeld gravity is a reformulation of the Eddington-inspired-Born-Infeld (EiBI) model under the mimetic approach. Due to the mimetic field, the theory contains non-trivial vacuum solutions different from those in Einstein gravity. We find that with the existence of the mimetic field, the spacelike singularity inside a Schwarzschild black hole could be altered to a lightlike singularity, even though the curvature invariants still diverge at the singularity. Furthermore, in this case, the maximal proper time for a timelike radially-infalling observer to reach the singularity is found to be infinite.