Could dark matter be a natural consequence of a dynamical universe?

TL;DR

This paper explores whether discrepancies between different definitions of gravitating mass in dynamical spacetimes could explain dark matter phenomena, questioning if such differences are inherent in general relativity.

Contribution

It investigates the conditions under which gravitating mass and physical mass-energy differ in non-stationary spacetimes within general relativity, highlighting potential implications for dark matter.

Findings

In stationary spacetimes, gravitating mass equals physical mass.

In dynamical spacetimes, the two masses may differ, suggesting a possible alternative explanation for dark matter.

Theoretical groundwork is laid for further study of mass definitions in evolving universes.

Abstract

We construct the gravitating mass of an isolated composite system on asymptotically-flat spacetimes within conventional general relativity and investigate when this quantity is well defined. For stationary spacetimes, this quantity is known to exactly equal the physical (ADM) mass. However, it remains an open question whether these two masses are equal in the absence of a timelike Killing vector. This is especially apropos since our universe has an `origin' and hence no such Killing vector. Further, if these masses failed to agree then composite systems could behave as if they had a `dark component,' whose gravitating mass would not equal the physical mass-energy present. The existence of such an apparent discrepancy is indeed ubiquitous in galaxies and galaxy clusters, though currently it is attributed to the presence of dark matter. We conclude that the theoretical question of the relation between these masses for dynamical spacetimes is ripe for attention.