Hairy black holes in DHOST theories: exploring disformal transformation as a solution generating method

Abstract

Solutions-generating methods based on field redefinitions, such as conformal\nmapping, play an important role in investigating exact solutions in modified\ngravity. In this work, we explore the possibility to use disformal field\nredefinitions to investigate new regions of the solution space of DHOST\ntheories. The crucial ingredient is to find suitable seed solutions to generate\nnew exact ones for DHOST theories. We first consider a seed solution of the\nEinstein-Scalar system describing a naked singularity. Under suitable\nassumptions, we derive a no-go result showing that no black hole solution can\nbe constructed from such a seed GR solution. Then, taking into account the\nstability of each degeneracy classes of quadratic DHOST theories under a\ngeneral disformal mapping, we consider two kinds of known black hole solutions\nas seed configurations: the Schwarzschild stealth solution and the non-stealth\nReissner-Nordstrom like solution. Restricting our considerations to invertible\ndisformal transformations, we show that building new hairy black hole solutions\nfrom the stealth solution associated to a constant kinetic term is also quite\nconstrained. We obtain new solutions which either are stealth or describe\nasymptotically locally flat black holes with a deficit solid angle. However,\nstarting from the non-stealth seed solution associated to a non constant\nkinetic term as well as a time-dependent scalar profile, we show that a\ndisformal transformation can introduce rather general modifications of the\nexterior geometry. Finally, we consider the construction of minimally modified\nhairy black hole solutions using a small disformal transformation. Further\napplications of this solution generating method should allow to provide new\nhairy rotating black hole solutions beyond the stealth sector useful for\nphenomenological investigations of compact objects beyond GR.\n