Intrinsic time gravity and the Lichnerowicz-York equation

Understand

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.