Disforming the Kerr metric

TL;DR

This paper constructs disformed Kerr black hole solutions from a scalar-tensor theory, revealing new non-Kerr features such as non-circularity and a novel horizon structure, thus expanding the landscape of black hole solutions.

Contribution

It introduces a method to generate disformed Kerr metrics with scalar hair, resulting in black holes that differ from Kerr in their geometric and horizon properties.

Findings

Disformed Kerr solutions have a ring singularity and are not Ricci flat.

The solutions exhibit non-circularity affecting their structure.

A new type of event horizon is identified inside the stationary limit surface.

Abstract

Starting from a recently constructed stealth Kerr solution of higher order scalar tensor theory involving scalar hair, we analytically construct disformal versions of the Kerr spacetime with a constant degree of disformality and a regular scalar field. While the disformed metric has only a ring singularity and asymptotically is quite similar to Kerr, it is found to be neither Ricci flat nor circular. Non-circularity has far reaching consequences on the structure of the solution. As we approach the rotating compact object from asymptotic infinity we find a static limit ergosurface similar to the Kerr spacetime with an enclosed ergoregion. However, the stationary limit of infalling observers is found to be a timelike hypersurface. A candidate event horizon is found in the interior of this stationary limit surface. It is a null hypersurface generated by a null congruence of light rays which are no longer Killing vectors. Under a mild regularity assumption, we find that the candidate surface is indeed an event horizon and the disformed Kerr metric is therefore a black hole quite distinct from the Kerr solution.