Exact Regular Planar Black Holes solutions in Bumblebee gravity

Abstract

We discuss possibilities of finding exact regular planar black hole solutions in bumblebee gravity with temporal and radial components of the bumblebee field. We consider quadratic and linear potentials, with vanishing and nonzero cosmological constants, respectively. The field equations determine the nonminimal coupling and the relations between the model parameters. Found solution produce regular planar black hole with planar deformation function. Analytical expressions for this functions has been found. This solutions free of singularities at the $r=0$.