Kerr–Schild metrics in teleparallel 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 f...
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SpringerOpen
2021-08-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-021-09551-5 |
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doaj-4cc75e7545784f589f9eaaff3fa894372021-08-29T11:16:14ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60441434-60522021-08-0181811110.1140/epjc/s10052-021-09551-5Kerr–Schild metrics in teleparallel gravityMarkus B. Fröb0Institut für Theoretische Physik, Universität LeipzigAbstract 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 $$f({\mathcal {T}})$$ f ( T ) gravity.https://doi.org/10.1140/epjc/s10052-021-09551-5 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Markus B. Fröb |
| spellingShingle |
Markus B. Fröb Kerr–Schild metrics in teleparallel gravity European Physical Journal C: Particles and Fields |
| author_facet |
Markus B. Fröb |
| author_sort |
Markus B. Fröb |
| title |
Kerr–Schild metrics in teleparallel gravity |
| title_short |
Kerr–Schild metrics in teleparallel gravity |
| title_full |
Kerr–Schild metrics in teleparallel gravity |
| title_fullStr |
Kerr–Schild metrics in teleparallel gravity |
| title_full_unstemmed |
Kerr–Schild metrics in teleparallel gravity |
| title_sort |
kerr–schild metrics in teleparallel gravity |
| publisher |
SpringerOpen |
| series |
European Physical Journal C: Particles and Fields |
| issn |
1434-6044 1434-6052 |
| publishDate |
2021-08-01 |
| description |
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 $$f({\mathcal {T}})$$ f ( T ) gravity. |
| url |
https://doi.org/10.1140/epjc/s10052-021-09551-5 |
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AT markusbfrob kerrschildmetricsinteleparallelgravity |
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