Non-perturbative spinning black holes in dynamical Chern-Simons gravity

TL;DR

This paper constructs exact spinning black hole solutions in dynamical Chern-Simons gravity, revealing deviations from Kerr black holes and confirming previous perturbative results for small coupling.

Contribution

It provides non-perturbative solutions for spinning black holes in dynamical Chern-Simons gravity, extending beyond prior perturbative analyses.

Findings

Black holes are stationary, axi-symmetric, and asymptotically flat.

Solutions possess a non-trivial scalar field and satisfy a generalized Smarr relation.

Results match perturbative solutions for small Chern-Simons coupling.

Abstract

Spinning black holes in dynamical Einstein-Chern-Simons gravity are constructed by directly solving the field equations, without resorting to any perturbative expansion. This model is obtained by adding to the Einstein-Hilbert action a particular higher-curvature correction: the Pontryagin density, linearly coupled to a scalar field. The spinning black holes are stationary, axi-symmetric, asymptotically flat generalisations of the Kerr solution of Einstein's gravity, but they possess a non-trivial (odd-parity) scalar field. They are regular on and outside the horizon and satisfy a generalized Smarr relation. We discuss the deviations from Kerr at the level of the spin and mass distribution, the horizon angular velocity, the ergo-region and some basic properties of geodesic motion. For sufficiently small values of the Chern-Simons coupling our results match those previously obtained using a perturbative approach.