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.
Highlights
That is associated to the existence of an additional Killing tensor [12]
Under a mild regularity assumption, we find that the candidate surface is an event horizon and the disformed Kerr metric is a black hole quite distinct from the Kerr solution
These mathematical properties pave the way to understanding, amongst other things, linear stability and quasi-normal modes and geodesics for black hole shadows
Summary
We start by constructing an explicit example of a disformal Kerr metric. By disformal Kerr metric, we mean a spacetime metric gμdiνsf which can be represented in the following way: gμdiνsf. Our starting block will be the stealth black hole solution found in [37] where the authors consider a subclass of DHOST Ia theory, and show that a nontrivial scalar field defined on the Kerr metric solves the equations of motion. The region of spacetime in between the ergosurface and the outer event horizon is the ergoregion of the original Kerr black hole, where one can have interesting physical effects such as the Penrose process. E, angular momentum L, rest mass m and Carter’s separation constant C (whose proof of existence gives integrability) The former two originate from the Killing vectors ∂t and ∂φ, while the latter two come from the existence of Killing tensors for the Kerr spacetime. Note that a similar observation has been noted in the case of Schwarzschild-de-Sitter metric in refs. [39, 44, 45] (see [49])
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