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

TL;DR

This paper investigates how disformal transformations can generate new black hole solutions in DHOST theories, revealing constraints and possibilities for creating hairy black holes with potential astrophysical relevance.

Contribution

It demonstrates the use of disformal field redefinitions to find new exact solutions in DHOST theories, including hairy black holes, and discusses the limitations and potential of this method.

Findings

No black hole solutions can be generated from naked singularity seed solutions.

Disformal transformations can produce stealth or asymptotically flat black holes with deficits.

New solutions can incorporate modifications to exterior geometry, useful for phenomenology.

Abstract

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