Cosmologically Coupled Black Holes with Regular Horizons

We present the most general and exact solution of Einstein's gravity sourced by an anisotropic fluid describing the cosmological embedding (CE) of a static and spherically-symmetric object, including black holes (BHs) or exotic compact objects, without radial energy influx and in an arbitrary Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology. This is done fully considering backreaction of the local geometry on the cosmological dynamics. Our solution is free of curvature singularities at the would-be BH event horizon, thus solving a main issue of the CE of BH solutions proposed so far. As a byproduct, we derive a new CE of the Schwarzschild BH - distinct from McVitties's original proposal - that is regular everywhere except at the central singularity.