# Static spherically symmetric solutions of Einstein field equations with radial dark matter

## TL;DR

This paper presents new static spherically symmetric solutions to Einstein's equations incorporating radial dark matter flows, explaining galaxy rotation curves without event horizons and exploring their implications for galactic models.

## Contribution

It introduces novel solutions with dark matter flows that prevent event horizon formation and produce realistic galaxy rotation curves within Einstein's framework.

## Key findings

- Solutions exhibit flat rotation curves at large distances.
- Dark matter prevents event horizon formation, creating high-redshift regions.
- Space-time structure differs from Schwarzschild near the gravitational radius.

## Abstract

We study a static spherically symmetric problem with a black hole and radially directed geodesic flows of dark matter. The obtained solutions have the following properties. At large distances, the gravitational field produces constant velocities of circular motion, i.e., flat rotation curves. At smaller distances, the field switches to Newtonian regime, then to Schwarzschild regime. Deviations from Schwarzschild regime start below the gravitational radius. The dark matter prevents the creation of event horizon, instead, a spherical region possessing extremely large redshift is created. The structure of space-time for the obtained solutions is investigated and the implications for the models of the galaxies are discussed.