Hamiltonian ADM Gravity in Non-Harmonic Gauges with Well Defined Non-Euclidean 3-Spaces: How Much Darkness can be Explained as a Relativistic Inertial Effect?

TL;DR

This paper explores how certain aspects of darkness in the universe might be explained as relativistic inertial effects within Einstein gravity, utilizing Hamiltonian ADM formalism and non-harmonic gauges to distinguish inertial from tidal gravitational effects.

Contribution

It introduces a Hamiltonian formulation of ADM gravity in non-harmonic gauges that clearly separates inertial effects from tidal gravitational degrees of freedom, highlighting the role of York time.

Findings

York time as a key inertial effect related to clock synchronization

Disentanglement of inertial and tidal gravitational degrees of freedom in Hamiltonian formalism

Potential explanation of darkness phenomena as relativistic inertial effects

Abstract

In special and general relativity the synchronization convention of distant clocks may be simulated with a mathematical definition of global non-inertial frames (the only ones existing in general relativity due to the equivalence principle) with well-defined instantaneous 3-spaces. For asymptotically Minkowskian Einstein space-times this procedure can be used at the Hamiltonian level in the York canonical basis, where it is possible for the first time to disentangle tidal gravitational degrees of freedom from gauge inertial ones. The most important inertial effect connected with clock synchronization is the York time {}^3K(\tau, \sigma^r), not existing in Newton gravity. This fact opens the possibility to describe some aspects of {\it darkness} as a relativistic inertial effect in Einstein gravity by means of a Post-Minkowskian reformulation of the Celestial Reference System ICRS.