On a problem of dark matter: A centrally symmetric distribution of a pseudoscalar field in the general relativity

TL;DR

This paper presents an exact solution in general relativity for a centrally symmetric pseudoscalar field distribution, suggesting it could explain dark matter phenomena like galaxy rotation curves and the cusp problem.

Contribution

It provides a new exact solution for a pseudoscalar field in general relativity, offering insights into dark matter distribution and galaxy dynamics.

Findings

Energy density is confined near the center and decreases slowly with radius.

The solution addresses the cusp problem in galaxy dark matter halos.

It explains galaxy rotation curves without requiring additional dark matter assumptions.

Abstract

A precise solution of the general relativity equations for centrally symmetric distribution of a pseudoscalar field with U(1) symmetry is presented. It is found that energy density of the field is restricted in the symmetry center and falls with radial distance at a much slower rate than in numerical simulations of dark matter haloes. This result can solve the cusp problem for galaxies and the problem of rotation curves for galaxy exteriors.