# Charged cosmological black holes: a thorough study of a family of solutions

## TL;DR

This paper thoroughly investigates a class of charged cosmological black holes described by the Shah-Vaidya solution, analyzing their causal structures, parameter space, and the influence of the Hubble factor on their properties.

## Contribution

It provides a detailed analysis of the Shah-Vaidya charged black hole solutions, including their causal structures and conditions for black holes versus naked singularities.

## Key findings

- Identification of parameter regions for well-behaved black holes and naked singularities.
- Causal diagrams illustrating all possible spacetime types.
- Theorem relating the Hubble factor's asymptotic behavior to causal properties.

## Abstract

We study a class of charged cosmological black holes defined by the Shah-Vaidya solution, which is similar to the McVittie solution but for a central object of nonzero electric charge. We show that the Shah-Vaidya metric is a solution of Einstein's equations with a cuscuton and a Maxwell fields as sources, as well as a mass parameter. We then analyze the possible causal structures of the solution under some few physically reasonable assumptions, and determine the regions in the parameter space corresponding to well behaved charged cosmological black holes and those corresponding to naked singularities. The asymptotic behavior of the Hubble factor $H(t)$ is also determinant to the causal properties of the spacetime and a theorem explaining its effect is stated. Examples of causal diagrams covering all the possibles types of spacetimes allowed by our initial assumptions are drawn and discussed.