Two-dimensional manifold with point-like defects

TL;DR

This paper investigates two-dimensional spherical extra spaces with point-like defects in multidimensional gravity, exploring their geometric properties and potential role as dark matter candidates.

Contribution

It introduces a family of stationary metrics with singular points on deformed spherical extra spaces, expanding understanding of their geometric and physical implications.

Findings

Existence of a family of stationary metrics with singularities.

Deformed extra spaces could serve as dark matter candidates.

Geometric analysis of point-like defects in extra dimensions.

Abstract

We study a class of two-dimensional compact extra spaces isomorphic to the sphere $S^2$ in the framework of multidimensional gravitation. We show that there exists a family of stationary metrics that depend on the initial (boundary) conditions. All these geometries have a singular point. We also discuss the possibility for these deformed extra spaces to be considered as dark matter candidates.