https://doi.org/10.1140/epjc/s10052-021-09551-5
Regular Article - Theoretical Physics
Kerr–Schild metrics in teleparallel gravity
Institut für Theoretische Physik, Universität Leipzig, Brüderstraße 16, 04103, Leipzig, Germany
Received:
11
March
2021
Accepted:
16
August
2021
Published online:
24
August
2021
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 
gravity.
© The Author(s) 2021
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