Gravity with extra dimensions and dark matter interpretation: A straightforward approach

TL;DR

This paper explores how extra dimensions in spacetime could explain dark matter phenomena by deriving an effective gravitational potential, providing a straightforward alternative to dark matter hypotheses with observational consistency.

Contribution

It presents a novel higher-dimensional model that explains galactic rotation curves without dark matter, using a factorizable metric and Einstein equations, validated against observational data.

Findings

Effective energy-momentum tensor derived from higher dimensions.

Galactic rotation curves match observations without dark matter.

Density profiles align with Newtonian potential predictions.

Abstract

Any connection between dark matter and extra dimensions can be cognizably evinced from the associated effective energy-momentum tensor. In order to investigate and test such relationship, a higher dimensional spacetime endowed with a factorizable general metric is regarded to derive a general expression for the stress tensor -- from the Einstein-Hilbert action -- and to elicit the effective gravitational potential. A particular construction for the case of six dimensions is provided, and it is forthwith revealed that the missing mass phenomenon may be explained, irrespective of the dark matter existence. Moreover, the existence of extra dimensions in the universe accrues the possibility of a straightforward mechanism for such explanation. A configuration which density profile coincides with the Newtonian potential for spiral galaxies is constructed, from a 4-dimensional isotropic metric plus extra-dimensional components. A Miyamoto-Nagai \emph{ansatz} is used to solve Einstein equations. The stable rotation curves associated to such system are computed, in full compliance to the observational data, without fitting techniques. The density profiles are reconstructed and compared to that ones obtained from the Newtonian potential.