# Exact black hole solutions in shift-symmetric quadratic degenerate higher-order scalar-tensor theories

## TL;DR

This paper derives exact black hole solutions within shift-symmetric quadratic degenerate higher-order scalar-tensor theories, revealing conditions on coupling functions that permit these solutions with regular scalar fields.

## Contribution

It provides the first explicit exact black hole solutions in this class of DHOST theories and clarifies the necessary conditions on the coupling functions for their existence.

## Key findings

- Exact Schwarzschild and Schwarzschild-(anti-)de Sitter solutions found.
- Conditions on coupling functions for solution existence derived.
- Scalar fields are regular at the black hole horizon.

## Abstract

We find various exact black hole solutions in the shift-symmetric subclass of the quadratic degenerate higher-order scalar-tensor (DHOST) theories with linearly time dependent scalar field whose kinetic term is constant. The exact solutions are the Schwarzschild and Schwarzschild-(anti-)de Sitter solutions, and the Schwarzschild-type solution with a deficit solid angle, which are accompanied by nontrivial scalar field regular at the black hole event horizon. We derive the conditions for the coupling functions in the DHOST Lagrangian that allow the exact solutions, clarify their compatibility with the degeneracy conditions, and provide general form of coupling functions as well as simple models that satisfy the conditions.