Reduced Conformal Geometrodynamics of Closed Manifolds

TL;DR

This paper develops a covariant approach to defining global time in closed manifolds using conformal geometrodynamics, involving Hamiltonian reduction and deparametrization, resulting in a non-conservative Hamiltonian system for gravity.

Contribution

It introduces a covariant global time definition based on conformal geometrodynamics and implements Hamiltonian reduction for closed manifolds.

Findings

Global intrinsic time linked to metric determinants

Hamiltonian reduction yields a non-conservative system

Hamiltonian equations of gravitational field derived in global time

Abstract

The global time is defined in covariant form under the condition of a constant mean curvature slicing of spacetime. The background static metric is taken in the tangent space. The global intrinsic time is identified with the logarithmic function of the mean value of the ratio of the square root of the metric determinants. The procedures of the Hamiltonian reduction and deparametrization of dynamical systems are implemented. The Hamiltonian system appears to be non-conservative. The Hamiltonian equations of motion of gravitational field in the global time are written.