General relativistic velocity: the alternative to dark matter

TL;DR

This paper proposes that general relativistic effects on velocity measurements in galaxy clusters could explain observed phenomena without dark matter, challenging the conventional Newtonian interpretation.

Contribution

It introduces a relativistic velocity formula for collapsing dust in weak gravity, offering an alternative explanation to dark matter for galaxy cluster dynamics.

Findings

Relativistic velocities differ significantly from Newtonian predictions in weak gravity.

Higher-than-expected velocities in galaxy clusters can be explained without dark matter.

Suggests new experimental tests of general relativity at smaller scales.

Abstract

We consider the gravitational collapse of a spherically symmetric ball of dust in the general relativistic weak gravity regime. The velocity of the matter as viewed by external observers is compared to the velocity gauged by local observers. While the comparison in the case of very strong gravity is seen to follow the pattern familiar from studies of test particles falling towards a concentrated mass, the case of weak gravity is very different. The velocity of the dust that is witnessed by external observers is derived for the critically open case and is seen to differ markedly from the expectations based upon Newtonian gravity theory. Viewed as an idealized model for a cluster of galaxies, we find that with the general relativistic velocity expression, the higher-than-expected constituent velocities observed can be readily correlated with the solely baryonic measure of the mass, obviating the need to introduce extraneous dark matter. Hitherto unexplained and subject-to-reinterpretation astrophysical phenomena could also be considered within this context. It is suggested that an attempt be made to formulate an experimental design at smaller scales simulating or realizing a collapse with the aim of implementing a new test of general relativity.