# Cosmological Solutions with Charged Black Holes

## TL;DR

This paper constructs exact cosmological solutions with multiple charged black holes, analyzing how electric charge influences the universe's expansion and providing new relativistic insights into charge effects on cosmological backreaction.

## Contribution

It introduces a method to generate initial data for multiple charged black holes in cosmology, extending previous solutions beyond extremality and exploring charge effects on cosmic evolution.

## Key findings

- Electric charge reduces the scale of the cosmological region.
- Constructed initial data for multiple charged black holes on a hypersphere.
- Generalized Majumdar-Papapetrou solutions beyond extremal limit.

## Abstract

We consider the problem of constructing cosmological solutions of the Einstein-Maxwell equations that contain multiple charged black holes. By considering the field equations as a set of constraint and evolution equations, we construct exact initial data for N charged black holes on a hypersphere. This corresponds to the maximum of expansion of a cosmological solution, and provides sufficient information for a unique evolution. We then consider the specific example of a universe that contains eight charged black holes, and show that the existence of non-zero electric charge reduces the scale of the cosmological region of the space. These solutions generalize the Majumdar-Papapetrou solutions away from the extremal limit of charged black holes, and provide what we believe to be some of the first relativistic calculations of the effects of electric charge on cosmological backreaction.