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arXiv · 1008.0591

Slowly rotating Kerr black hole as a solution of Einstein-Cartan gravity extended by a Chern-Simons term

Mauro Cambiaso·Luis F. Urrutia
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Abstract

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 $β$ which codifies the CS coupling. Starting from a torsionless zeroth-order vacuum solution we derive the second-order differential equation for the $\mathcal{O}(β)$ corrections to the metric, for an arbitrary embedding parameter. Furthermore we can show that the slowly rotating Kerr metric is an $\mathcal{O}(β)$ solution of the system either in the canonical or the axial embeddings.

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Mauro Cambiaso, Luis F. Urrutia. 2010-08-03. Slowly rotating Kerr black hole as a solution of Einstein-Cartan gravity extended by a Chern-Simons term. https://doi.org/10.1142/9789814327688_0043

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