Stable black hole solutions with cosmological hair

Dynamical dark energy theories generically introduce a time-dependent field that causes the accelerated expansion of the Universe on large scales. When embedding black hole solutions in such a cosmological spacetime, this time dependence naturally gives rise to cosmological hair, i.e. the local black hole physics is no longer controlled by just the mass and spin of the black hole, but also impacted by the dark energy field. However, known such solutions are unstable. Focusing on the cubic Galileon as a concrete and illustrative example, we discuss the restrictions imposed on physical solutions by their regularity and stability in detail. We explicitly derive regular and stable solutions, that both recover the desired cosmological long-range behaviour and give rise to well-behaved short-range dynamics around black holes. We show how the nature of the scalar hair around these local black hole solutions encodes cosmological information, highlighting novel and tantalising prospects of directly probing cosmological dynamics with black hole observations.