Eur. Phys. J. C (2018) 78: 59
https://doi.org/10.1140/epjc/s10052-018-5556-z

Regular Article - Theoretical Physics

Black hole solutions in mimetic Born-Infeld gravity

¹ Department of Physics and Center for Theoretical Sciences, National Taiwan University, Taipei, 10617, Taiwan
² LeCosPA, National Taiwan University, Taipei, 10617, Taiwan
³ Department of Theoretical Physics, University of the Basque Country UPV/EHU, P.O. Box 644, 48080, Bilbao, Spain
⁴ IKERBASQUE, Basque Foundation for Science, 48011, Bilbao, Spain
⁵ Kavli Institute for Particle Astrophysics and Cosmology, SLAC National Accelerator Laboratory, Stanford University, Stanford, CA, 94305, USA

^* e-mail: b97202056@gmail.com

Received: 4 November 2017
Accepted: 15 January 2018
Published online: 23 January 2018

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.