Slowly moving black holes in Lorentz-violating scalar-tensor gravity

TL;DR

This paper investigates slowly moving black holes within Lorentz-violating scalar-tensor theories, deriving a unified master equation for perturbations, and finds solutions regular outside the universal horizon that are independent of specific model functions.

Contribution

It generalizes previous studies by deriving a master equation for coupled metric and scalar perturbations in a broad class of scalar-tensor theories with Lorentz violation.

Findings

Derived a single master equation for perturbations.

Found solutions regular outside the universal horizon.

Results are independent of the arbitrary function in the theory.

Abstract

A scalar field with a timelike gradient defines a preferred slicing. This occurs even in a non-cosmological setup in scalar-tensor theories such as khronometric theory. We study a black hole moving slowly relative to the preferred slicing defined by the scalar field. We consider a family of higher-order scalar-tensor theories that extend khronometric theory. The action is characterized by one constant parameter and one arbitrary function of the kinetic term of the scalar field. A slowly moving black hole is described by a dipole perturbation of a black hole at rest. We treat the metric and scalar-field perturbations consistently, derive a single master equation for the coupled system, and reconstruct the metric for a slowly moving black hole from the master variable. In this way, we revisit and generalize the previous studies. For generic theories in the family we consider, we find a solution that is regular outside the universal horizon and agnostic to the arbitrary function in the action.