Charged spherically symmetric and slowly rotating charged black hole solutions in bumblebee gravity

TL;DR

This paper derives new charged black hole solutions in bumblebee gravity, analyzes their properties, and studies how electric charge and Lorentz-violating parameters influence black hole shadows, revealing specific effects on shadow size and distortion.

Contribution

It introduces charged black hole solutions in bumblebee gravity and examines the impact of Lorentz violation on their shadow characteristics.

Findings

Shadow radius decreases with Lorentz-violating and charge parameters.

Shadow distortion increases with Lorentz-violating and charge parameters.

Solutions include Reissner-Nordström-like and Kerr-Newman-like black holes.

Abstract

In this paper, we present charged spherically symmetric black hole solutions and slowly rotating charged solutions in bumblebee gravity with and without a cosmological constant. The static spherically symmetric solutions describe the Reissner-Nordstr\"om-like black hole and ReissnerNordstr\"om-(anti) de Sitter-like black hole, while the stationary and axially symmetric soltuions describe Kerr-Newman-like black hole and Kerr-Newman-(anti) de Sitter-like black hole. We utilize the Hamilton-Jacobi formalism to study the shadows of the black holes. Additionally, we investigate the effect of the electric charge and Lorentz-violating parameters on the radius of the shadow reference circle and the distortion parameter. We find that the radius of the reference circle decreases with the Lorentz-violating parameter and charge parameter, while the distortion parameter increases with the Lorentz-violating parameter and the charge parameter.