McVittie's Legacy: Black Holes in an Expanding Universe

TL;DR

This paper proves that certain solutions to Einstein's equations describe regular black holes embedded in expanding universe models, with specific conditions leading to regular or singular horizons.

Contribution

It demonstrates that McVittie's solutions include regular black holes in cosmologies with a positive cosmological constant, extending understanding of black holes in expanding universes.

Findings

Solutions are regular outside the horizon with a positive cosmological constant.

Solutions asymptote to Schwarzschild-de Sitter geometry near the horizon.

Without a positive cosmological constant, solutions have weak null singularities.

Abstract

We prove that a class of solutions to Einstein's equations---originally discovered by G. C. McVittie in 1933---includes regular black holes embedded in Friedman-Robertson-Walker cosmologies. If the cosmology is dominated at late times by a positive cosmological constant, the metric is regular everywhere on and outside the black hole horizon and away from the big bang singularity, and the solutions asymptote in the future and near the horizon to the Schwarzschild-de Sitter geometry. For solutions without a positive cosmological constant the would-be horizon is a weak null singularity.