Cosmologically Coupled Black Holes with Regular Horizons

TL;DR

This work tackles the problem of curvature singularities in cosmologically embedded black holes by constructing the most general exact CE solution for an anisotropic fluid with backreaction from the cosmological background, encoded through the cosmological density $\rho_{\text c}$. A local Misner–Sharp mass framework is developed, with a companion function $\mathcal{M}(r,a)$ governing the solution, yielding regular spacetimes at the would-be horizon. The authors present two BH CE classes: a Schwarzschild CE distinct from McVittie and a horizon-regular CE that remains free of horizon singularities due to backreaction; the latter extends to nonsingular BHs with de Sitter cores. Energy-condition analysis shows WEC/NEC can hold outside the exterior, while DEC and near-horizon NEC may be violated depending on the cosmological equation of state, all within an interpretation of the anisotropic fluid as an effective description of inhomogeneities. Overall, the paper provides a consistent framework for horizon-regular cosmological embeddings and introduces a new Schwarzschild CE, with implications for BH cosmology and tests of gravity.

Abstract

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.