Cosmological black holes from self-gravitating fields

Abstract

Both cosmological expansion and black holes are ubiquitous features of our observable Universe, yet exact solutions connecting the two have remained elusive. To this end, we study self-gravitating classical fields within dynamical spherically symmetric solutions that can describe black holes in an expanding universe. After attempting a perturbative approach of a known black-hole solution with scalar hair, we show by exact methods that the unique scalar field action with first-order derivatives that can source shear-free expansion around a black hole requires noncanonical kinetic terms. The resulting action is an incompressible limit of $k$-essence, otherwise known as the cuscuton theory, and the spacetime it describes is the McVittie metric. We further show that this solution is an exact solution to the vacuum Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity with anisotropic Weyl symmetry.