# Black Holes in an Expanding Universe

## TL;DR

This paper presents an exact solution describing maximally charged black holes embedded in an expanding universe with arbitrary equation of state, involving a scalar field and two U(1) gauge fields, with a focus on horizon properties and temperature.

## Contribution

It introduces a new exact Einstein-scalar-Maxwell solution for black holes in an expanding universe with a scalar field and two gauge fields, including horizon analysis and temperature calculation.

## Key findings

- Regular horizon depends on energy density ratio
- Horizon remains static due to force balance
- Black hole temperature is explicitly calculated

## Abstract

An exact solution representing black holes in an expanding universe is found. The black holes are maximally charged and the universe is expanding with arbitrary equation of state. It is an exact solution of the Einstein-scalar-Maxwell system, in which we have two Maxwell-type U(1) fields coupled to the scalar field. The potential of the scalar field is an exponential. We find a regular horizon, which depends on one parameter (the ratio of the energy density of U(1) fields to that of the scalar field). The horizon is static because of the balance on the horizon between gravitational attractive force and U(1) repulsive force acting on the scalar field. We also calculate the black hole temperature.