Gravitational wave signatures from dark sector interactions
  We show that the gravitational waves generated by the perturbations of
general relativistic black holes can be considered as a direct probe of the
existence of dark sector interactions. Working within the framework of
Horndeski theory and linear perturbations, we show that dark sector
interactions effectively reduce to an interaction charge that influences both
scalar and tensor waveforms. Furthermore, we show that the total dark matter
field, including the effects of dark sector interactions, satisfies a
conservation equation embodying the equivalence principle. We exploit this
realization to setup the Regge-Wheeler equation and the coupled Zerilli and
scalar wave equations for a Schwarzschild-(anti) de Sitter black hole. We then
present numerical integration of the coupled even-parity wave equations for the
case of a dark matter particle falling straight down into a Schwarzschild black
hole.
