Can a tensorial analogue of gravitational force explain away the galactic rotation curves without dark matter?

TL;DR

This paper proposes a tensorial modification of gravity using the Lanczos tensor field, which can explain galactic rotation curves without dark matter, challenging the need for dark matter in astrophysics.

Contribution

It introduces a relativistic analogue of gravitational force via the Lanczos tensor, offering a novel explanation for galaxy rotation curves within general relativity.

Findings

Lanczos tensor generates a modified acceleration law.

The modified law explains flat rotation curves without dark matter.

Supports alternative gravity theories to dark matter hypothesis.

Abstract

The dark matter problem is one of the most pressing problems in modern physics. As there is no well-established claim from a direct detection experiment supporting the existence of the illusive dark matter that has been postulated to explain the flat rotation curves of galaxies, and since the whole issue of an alternative theory of gravity remains controversial, it may be worth to reconsider the familiar ground of general relativity (GR) itself for a possible way out. It has recently been discovered that a skew-symmetric rank-three tensor field - the Lanczos tensor field - that generates the Weyl tensor differentially, provides a proper relativistic analogue of the Newtonian gravitational force. By taking account of its conformal invariance, the Lanczos tensor leads to a modified acceleration law which can explain, within the framework of GR itself, the flat rotation curves of galaxies without the need for any dark matter whatsoever.