Gravitational theoretical development supporting MOND

TL;DR

This paper develops a relativistic geometric framework that modifies Einstein's equations, providing a theoretical basis for MOND to explain galaxy rotation curves without dark matter.

Contribution

It introduces a conformal geometric approach within general relativity that explicitly supports MOND through a new covariant acceleration potential.

Findings

Reproduces galaxy rotation curves without dark matter

Matches observed velocity distributions at large distances

Aligns large distance expansion rate with shock wave speed

Abstract

Conformal geometry is considered within a general relativistic framework. An invariant distant for proper time is defined and a parallel displacement is applied in the distorted space-time, modifying Einstein's equation appropriately. A particular solution is introduced for the covariant acceleration potential that matches the observed velocity distribution at large distances from the galactic centre, i.e. Modified Newtonian Dynamics (MOND). This explicit solution, of a general framework that allows both curvature and explicit local expansion of space-time, thus reproduces the observed flattening of galaxys' rotation curves without the need to assume the existence of dark matter. The large distance expansion rate is found to match the speed of a spherical shock wave.