Kerr-Schild metrics in teleparallel gravity

TL;DR

This paper extends the Kerr-Schild ansatz to teleparallel gravity, deriving solutions for rotating black holes and exploring their properties within this framework, including implications for $f(T)$ gravity.

Contribution

It introduces a novel extension of the Kerr-Schild ansatz to teleparallel gravity and analyzes the resulting black hole solutions and their dependence on tetrad choices.

Findings

Kerr-Schild ansatz can be extended to teleparallel gravity.

Rotating black hole solutions are derived in this framework.

Any Kerr-Schild solution with flat background also solves $f(T)$ gravity.

Abstract

We show that the Kerr-Schild ansatz can be extended from the metric to the tetrad, and then to teleparallel gravity where curvature vanishes but torsion does not. We derive the equations of motion for the Kerr-Schild null vector, and describe the solution for a rotating black hole in this framework. It is shown that the solution depends on the chosen tetrad in a non-trivial way if the spin connection is fixed to be the one of the flat background spacetime. We show furthermore that any Kerr-Schild solution with a flat background is also a solution of $f(\mathcal{T})$ gravity.