In the Einstein-Cartan formulation, an iterative procedure to find solutions in nondynamical Chern-Simons gravity in vacuum is proposed. The iterations, in powers of a small parameter $\beta$ which codifies the Chern-Simons coupling, start from an arbitrary torsionless solution of Einstein equations. With Schwarzschild as the zeroth-order choice, we derive a second-order differential equation for the $\mathcal{O}(\beta )$ corrections to the metric, for an arbitrary zeroth-order embedding parameter. In particular, the slowly rotating Kerr metric is an $\mathcal{O}(\beta )$ solution in either the canonical or the axial embeddings.

• Received 15 May 2010

DOI:https://doi.org/10.1103/PhysRevD.82.101502