Dark matter effects in vacuum spacetime

TL;DR

This paper proposes a toy model where vacuum spacetime exhibits effects similar to dark matter, suggesting dark matter could be a dynamical consequence of spacetime curvature rather than actual matter.

Contribution

It introduces a model demonstrating how dark matter effects can arise in vacuum spacetime without real matter, offering a new perspective on dark matter's nature.

Findings

Test mass trajectories mimic dark matter effects

No actual matter or energy is present in the model

Dark matter effects may be due to spacetime curvature

Abstract

We analyze a toy model describing an empty spacetime in which the motion of a test mass (and the trajectories of photons) evidence the presence of a continuous and homogeneous distribution of matter; however, since the energy-momentum tensor vanishes, no real matter or energy distribution is present at all. Thus, a hypothetical observer will conclude that he is immersed in some sort of dark matter, even though he has no chance to directly detect it. This suggests yet another possibility of explaining the elusive dark matter as a purely dynamical effect due to the curvature of spacetime.