Intrinsic time gravity and the Lichnerowicz-York equation

Abstract

We investigate the effect on the Hamiltonian structure of general relativity of choosing an intrinsic time to fix the time slicing. 3-covariance with momentum constraint is maintained, but the Hamiltonian constraint is replaced by a dynamical equation for the trace of the momentum. This reveals a very simple structure with a local reduced Hamiltonian. The theory is easily generalised; in particular, the square of the Cotton-York tensor density can be added as an extra part of the potential while at the same time maintaining the classic 2 + 2 degrees of freedom. Initial data construction is simple in the extended theory; we get a generalised Lichnerowicz-York equation with nice existence and uniqueness properties. Adding standard matter fields is quite straightforward.

4 pages

References in corpus (4)

• Quantum Gravity at a Lifshitz Point
• Relativity without relativity
• General Relativity without paradigm of space-time covariance, and resolution of the problem of time
• Scaling up the extrinsic curvature in gravitational initial data

Cited by in corpus (13)

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• Cosmic time and reduced phase space of General Relativity
• Minimally modified gravity with auxiliary constraints formalism
• Intrinsic time gravity, heat kernel regularization, and emergence of Einstein's theory
• Quantum geometrodynamics with intrinsic time development
• Gravitational waves in Intrinsic Time Geometrodynamics
• Intrinsic Time Deparameterization of The Canonical Connection Dynamics of General Relativity
• Reduced Conformal Geometrodynamics of Closed Manifolds
• Cosmic time and the initial state of the universe