Apparent horizons in cosmologically-embedded black holes

TL;DR

This paper derives exact solutions for non-singular black holes embedded in cosmological backgrounds, analyzing their apparent horizons' evolution with redshift and contrasting them with event horizons.

Contribution

It introduces new exact solutions for cosmologically embedded non-singular black holes and examines the evolution of their apparent horizons over cosmic time.

Findings

Apparent horizons are larger than event horizons in these models.

The apparent horizon size increases monotonically with redshift.

Explicit formulas and numerical results are provided for specific black hole models.

Abstract

We present exact solutions for the cosmological embedding of a broad class of non-singular black holes, demonstrating that these objects exhibit an apparent horizon. The evolution of the latter is analyzed as a function of the cosmological redshift $z$. We show that its size exceeds that of the event horizon of an isolated black hole and increases monotonically with increasing $z$. Explicit formulas and numerical results are provided for the specific cases of the Hayward and Fan $\&$ Wang non-singular black-hole models. Furthermore, we explore the distinct dynamical roles of the event and apparent horizons, highlighting connection between the latter and the recently identified cosmological mass shift in non-singular black holes.