Compact Hamiltonian Formulation of Metric Gravity: Properties and Applications

A compact Hamiltonian formulation of metric gravity is developed, investigated and applied to some relevant problems. This new Hamiltonian formulation is closely related (by some canonical transformations of the dynamical variables) to the two known and only successful Hamiltonian formulations of the metric gravity proposed earlier (by Dirac and by the author’s group). In reality, our set of natural and canonical dynamical variables in metric gravity allows one to reduce both canonical and total Hamiltonians to very compact expressions, each being a pure quadratic form in the spatial momenta $$p^{mn}$$ . Analytical formulas for the primary and secondary constraints are also compact and physically transparent. In general, our new approach transforms the traditional Hamiltonian formulations of metric gravity into a simple procedure which allows one to solve a number of long-standing problems.