Making sense of the bizarre behaviour of horizons in the McVittie spacetime

TL;DR

This paper analyzes the unusual behavior of horizons in McVittie spacetime, comparing it with Schwarzschild-de Sitter spacetime, revealing how different cosmic backgrounds affect horizon existence and behavior over time.

Contribution

It provides a detailed discussion of horizon dynamics in McVittie spacetime, highlighting the impact of cosmic background composition on horizon properties and their evolution.

Findings

In dust-dominated universes, black hole horizons cannot form early on.

Phantom-dominated universes cause a reversed horizon behavior.

Horizon behavior depends critically on the background universe type.

Abstract

The bizarre behaviour of the apparent (black hole and cosmological) horizons of the McVittie spacetime is discussed using, as an analogy, the Schwarzschild-de Sitter-Kottler spacetime (which is a special case of McVittie anyway). For a dust-dominated "background" universe, a black hole cannot exist at early times because its (apparent) horizon would be larger than the cosmological(apparent) horizon. A phantom-dominated "background" universe causes this situation, and the horizon behaviour, to be time-reversed.