The stealth Kerr solution in the bumblebee gravity

TL;DR

This paper derives a Kerr black hole solution with a nontrivial vector field in the bumblebee gravity model, demonstrating the solution's generation via the Newman-Janis algorithm and highlighting its simplicity within vector-tensor theories.

Contribution

It presents the first Kerr solution with a vector field in the bumblebee model and shows how it can be generated from a spherical solution using the Newman-Janis algorithm.

Findings

Kerr solution with vector field in bumblebee gravity found.

Vector field generated from spherical solution via Newman-Janis algorithm.

Solution exemplifies a simple black-hole solution in vector-tensor theories.

Abstract

In this paper, we find Kerr solution accompanied with a nontrivial vector field as a solution to one of the simplest vector-tensor theories of gravity, namely the bumblebee model with an intriguing coupling constant between the Ricci curvature tensor and the vector field. We also demonstrate that the accompanied vector field can be generated via the Newman-Janis algorithm from a simple spherical vector field, which together with the Schwarzschild metric constitutes a solution to the same bumblebee model. It is probably the simplest example of a theory and its black-hole solutions for the Newman-Janis algorithm to hold except for general relativity.