Compact objects of spherical symmetry in beyond Horndeski theories

TL;DR

This paper investigates black hole solutions in beyond Horndeski theories with shift symmetry, deriving compact field equations, exploring solutions under parity symmetry, and presenting a method for generating diverse black hole and wormhole configurations.

Contribution

It introduces a new compact formulation of field equations in beyond Horndeski theories and provides a systematic approach to find black hole solutions with various asymptotics.

Findings

Multiple black hole solutions with Reissner-Nordstrom behavior.

New methods to generate asymptotically flat and AdS black holes.

Disformal transformations can produce wormholes and black holes.

Abstract

We analyse in all generality beyond Horndeski theories of shift symmetry in a static and spherically symmetric spacetime. By introducing four auxiliary functions, we write the field equations in a particularly compact form. We show that assuming additionally parity symmetry renders the system directly integrable giving multiple families of black-hole solutions. These have typically an asymptotically-flat Reissner-Nordstrom behaviour, and emerge in the presence of a canonical kinetic term for the scalar field. In the absence of parity symmetry, we present a general method which allows us to integrate the field equations by choosing the form of only one coupling function and an auxiliary quantity. This method leads to asymptotically flat and AdS black hole solutions with differing properties. We finally discuss disformal transformations within this context as a means of obtaining wormhole and black hole solutions in different theories.