Horndeski meets McVittie: A scalar field theory for accretion onto cosmological black holes

TL;DR

This paper demonstrates that a subclass of Horndeski scalar-tensor theories admits the generalized McVittie spacetime as an exact solution, revealing new insights into black hole and cosmological background interactions.

Contribution

It establishes a link between the McVittie solution and Horndeski theories, introducing a duality via disformal transformation and extending understanding of scalar field interactions with black holes.

Findings

Generalized McVittie spacetime is an exact solution of a Horndeski subclass.

Higher-order kinetic gravity braiding generates energy transfer between black hole and universe.

Disformal transformation connects cuscuton theory to extended Horndeski actions.

Abstract

We show that the generalized McVittie spacetime, which represents a black hole with time-dependent mass in an expanding universe, is an exact solution of a subclass of the Horndeski family of actions. The heat-flow term responsible for the energy transfer between the black hole and the cosmological background is generated by the higher-order kinetic gravity braiding term, which generalizes the cuscuton action that yields McVittie with constant mass as a solution. Finally, we show that this generalization can be understood in terms of a duality realized by a disformal transformation, connecting the cuscuton field theory to an extension of the Horndeski action which does not propagate any scalar degrees of freedom. Our finding opens a novel window into studies of non-trivial interactions between dark energy/modified gravity theories and astrophysical black holes.