On Rotating Black Holes in DHOST Theories

TL;DR

This paper constructs new rotating black hole solutions in DHOST theories using disformal transformations, revealing unique geometrical properties and breaking Kerr's hidden symmetries, thus advancing understanding of alternative gravity models.

Contribution

It introduces a novel disformal solution-generating method to produce rotating black holes in DHOST theories, including the first analytic non-stealth solution with explicit parameters.

Findings

The disformed Kerr solution is not Ricci flat and has the same singularity as Kerr.

The solution admits an ergoregion and is asymptotically flat.

The Kerr hidden symmetry is broken in the disformed geometry.

Abstract

Using the disformal solution-generating method, we construct new axisymmetric solutions in Degenerate Higher Order Scalar Tensor (DHOST) theories. The method consists in first considering a "seed" known solution in DHOST theories and then performing a disformal transformation of the metric to obtain a new solution. In vacuum, the two solutions are equivalent but they become physically inequivalent when one considers coupling to matter. In that way, we "disform" the stealth Kerr black hole solution and we obtain a first analytic rotating non-stealth solution in DHOST theories, while the associated scalar field is time-dependent with a constant kinetic density. The new solution is characterized by three parameters: the mass, the spin and the disformal parameter which encodes the deviation with respect to the Kerr geometry. We explore some geometrical properties of the novel disformed Kerr geometry which is no more Ricci flat, has the same singularity as the Kerr metric, admits an ergoregion, and is asymptotically flat. Moreover, the hidden symmetry of the Kerr solution is broken, providing an example of a non-circular geometry in a higher order theory of gravity. We also discuss geodesic motions and compute its (disformed) null directions which are interesting tools to understand the causal structure of the geometry. In addition, to illustrate again the potentiality of the disformal solution-generating method, we present another axisymmetric solution for DHOST theories obtained from a disformal transformation of the generalized Kerr solution of Einstein-Scalar gravity.