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Slowly rotating Kerr black hole as a solution of Einstein-Cartan gravity extended by a Chern-Simons term. (English) Zbl 1237.83023

Kostelecký, V. Alan (ed.), CPT and Lorenz symmetry. Proceedings of the 5th meeting, Bloomington, IN, USA, 28 June – 2 July 2010. Hackensack, NJ: World Scientific (ISBN 978-981-4327-67-1/hbk; 978-981-4327-68-8/ebook). 219-223 (2011).
Summary: We consider the nondynamical Chern-Simons (CS) modification to General Relativity (GR) in the framework of the Einstein-Cartan formulation, as providing a way to incorporate a slowly rotating Kerr black hole in the space of solutions. Our proposal lies on considering the CS term as a source of torsion and on an iterative procedure to look for vacuum solutions of the system, by expanding the tetrad, the connection and the embedding parameter, in powers of a dimensionless small parameter \(\beta \) which codifies the CS coupling. Starting from a torsionless zeroth-order vacuum solution we derive the second-order differential equation for the \(\mathcal O(\beta)\) corrections to the metric, for an arbitrary embedding parameter. Furthermore we can show that the slowly rotating Kerr metric is an \(\mathcal O(\beta)\) solution of the system either in the canonical or the axial embeddings.
For the entire collection see [Zbl 1234.81019].

MSC:

83C57 Black holes
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