Towards rotating non-circular black holes in string-inspired gravity

TL;DR

This paper investigates the possibility of rotating non-circular black holes in string-inspired gravity theories, finding that such solutions are likely non-existent due to singularities or incompatibility with stationarity.

Contribution

It demonstrates that dynamical scalar fields in these theories cannot support regular, stationary, rotating non-circular black holes, highlighting limitations of these models.

Findings

Scalar fields can be time-dependent but lead to singular horizons.

Regular stationary solutions only include known black hole solutions.

Rotating non-circular black holes are unlikely to exist in these theories.

Abstract

We study stationary slowly rotating black holes, up to quadratic order in the spin angular momentum, in dynamical Chern-Simons gravity and shift symmetric Einstein scalar Gauss-Bonnet gravity, as models of string-inspired gravities. These gravity theories modify general relativity by introducing dynamical scalar fields coupled with curvature invariants. We show that the linear time dependence of the scalar fields is allowed from the stationarity of the effective stress energy tensors. However, these time dependent scalar fields yield singular behavior of the metric functions at the black hole horizons, or they are incompatible with the stationarity of the spacetimes. Thus, these gravity theories admit only known solutions as regular stationary solutions. Our results suggest the non-existence of rotating non-circular black holes in these gravity theories.