Intrinsic Time in Geometrodynamics of Closed Manifolds

Abstract

The global time in Geometrodynamics is defined in a covariant under diffeomorphisms form. An arbitrary static background metric is taken in the tangent space. The global intrinsic time is identified with the mean value of the logarithm of the square root of the ratio of the metric determinants. The procedures of the Hamiltonian reduction and deparametrization of dynamical systems are implemented. The explored Hamiltonian system appeared to be non-conservative. The Hamiltonian equations of motion of gravitational field in the global time are written. Relations between different time intervals (coordinate, intrinsic, proper) are obtained.