Regular black holes via the Kerr-Schild construction in DHOST theories

Abstract

We extend the standard Kerr-Schild solution generating method to higher order\nscalar tensor theories that are shift-invariant for the scalar field. Certain\ndegeneracy conditions, crucial for the absence of Ostrogradski ghosts, are\nfound to be required for the validity of the Kerr-Schild ansatz while on the\nother hand, theories with no parity symmetry are excluded from the solution\ngenerating method. The extended Kerr-Schild symmetry turns out to be a very\nuseful tool to easily construct black hole solutions from simple seed\nconfigurations. In particular, the generating method developed is adapted to\nconstruct generic black holes but also regular black hole solutions within\nDegenerate Higher Order Scalar Tensor (DHOST) theories. As a particular example\nwe show how to construct explicitly the Hayward metric as a solution to a\nspecific DHOST theory.\n