Peculiar anisotropic stationary spherically symmetric solution of Einstein equations

TL;DR

This paper introduces an exact, static, spherically symmetric solution to Einstein's equations with no mass but non-zero spacelike stress-energy components, potentially explaining dark matter effects.

Contribution

It presents a novel solution with unusual stress-energy properties that can model gravitational phenomena typically attributed to dark matter.

Findings

The solution describes gravitational effects without mass.

It aligns with dark matter phenomenology.

It suggests non-zero spacelike stress-energy components as relevant to dark matter.

Abstract

Motivated by studies on gravitational lenses, we present an exact solution of the field equations of general relativity, which is static and spherically symmetric, has no mass but has a non-vanishing spacelike components of the stress-energy-momentum tensor. In spite of its strange nature, this solution provides with non-trivial descriptions of gravitational effects. We show that the main aspects found in the \emph{dark matter phenomena} can be satisfactorily described by this geometry. We comment on the relevance it could have to consider non-vanishing spacelike components of the stress-energy-momentum tensor ascribed to dark matter.