# Angular momentum, mass and charge inequalities for black holes in Einstein-Maxwell gravity with dark matter sector

## TL;DR

This paper derives inequalities relating angular momentum, mass, and charge for black holes in Einstein-Maxwell gravity extended with a dark matter sector, showing dark matter significantly influences black hole mass growth and properties.

## Contribution

It introduces new inequalities in Einstein-Maxwell gravity with a dark matter sector, highlighting the impact of dark matter on black hole characteristics.

## Key findings

- Dark matter sector affects black hole mass growth.
- Charge and size inequalities depend on dark matter coupling.
- Dark matter may explain early supermassive black holes.

## Abstract

Angular momentum and mass-charge inequalities for axisymmetric maximal time-symmetric initial data in Einstein-Maxwell gravity with dark matter sector were derived. The dark matter sector is mimicked by another U(1)-gauge field coupled to the ordinary Maxwell one. We assume that data set with two asymptotically flat regions is given on smooth simply connected manifold. One also pays attention to the area momentum charge inequalities for a closed orientable two-dimensional spacelike surface embedded in the spacetime of the considered theory. It turned out that the addition of dark matter sector influences to the great extent on the growth of the black hole masses. This fact may be responsible for the existence of the recently detected supermassive objects at relatively short time after Big Bang. The inequalities binding the charge of the body (black hole) and its size were also investigated. It turns out that the estimation depends on the coupling constant of the ordinary matter to the dark matter sector.