  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.
