Stability of a black hole and the speed of gravity waves within
  self-tuning cosmological models
  The gravitational wave event GW170817 together with its electromagnetic
counterparts constrains the speed of gravity to be extremely close to that of
light. We first show, on the example of an exact Schwarzschild-de Sitter
solution of a specific beyond-Horndeski theory, that imposing the strict
equality of these speeds in the asymptotic homogeneous Universe suffices to
guarantee so even in the vicinity of the black hole, where large curvature and
scalar-field gradients are present. We also find that the solution is stable in
a range of the model parameters. We finally show that an infinite class of
beyond-Horndeski models satisfying the equality of gravity and light speeds
still provide an elegant self-tuning: The very large bare cosmological constant
entering the Lagrangian is almost perfectly counterbalanced by the
energy-momentum tensor of the scalar field, yielding a tiny observable
effective cosmological constant.
