Dark Matter as a Relativistic Inertial Effect in Einstein Canonical Gravity?

TL;DR

This paper explores how dark matter effects in galaxy rotation curves can be interpreted as relativistic inertial effects related to the York time in Einstein canonical gravity, offering a new perspective on dark matter phenomena.

Contribution

It introduces a novel interpretation of dark matter as a relativistic inertial effect linked to the York time within the Hamiltonian formulation of Einstein gravity.

Findings

Dark matter effects can be explained by specific choices of York time.

The York time acts as an inertial gauge variable influencing gravitational phenomena.

The approach connects relativistic inertial effects with observable galaxy rotation curves.

Abstract

After the study of non-inertial frames in special relativity with emphasis on the problem of clock synchronization (i.e. of how to define 3-space), an overview is given of Einstein canonical gravity in the York canonical basis and of its Hamiltonian Post-Minkowskian (PM) linearization in 3-orthogonal gauges. It is shown that the York time (the trace of the extrinsic curvature of 3-spaces) is the inertial gauge variable describing the general relativistic remnant of the clock synchronization gauge freedom. The dark matter implied by the rotation curves of galaxies can be explained with a choice of the York time implying a PM extension of the Newtonian celestial frame ICRS.