Internal-external-dynamics decoupling in canonical general relativity

Gerhard Schäfer

Gerhard Schäfer is a retired professor at the University of Jena. His main scientific interests are equations of motion in general
relativity and their applications in astronomy and astrophysics.

Research on general-relativistic equations of motion based on Hamiltonian or canonical frameworks is not quite a main-stream doing; likely because of the all-over covariance of the theory and canonical is just not covariant but rather quite the opposite. Covariance under spacetime coordinate transformations makes the theory a spacetime-local one with its local scalars, vectors and tensors, the canonical picture on the other side is at home in the phase space of the dynamics which combines position and momentum variables. Crucial object-changing operations in spacetime are covariant derivatives, crucial ones in phase space are Poisson brackets.

What is the benefit of performing research in general relativity within a canonical framework? Let us concentrate on gravitating systems living in asymptotically flat spacetimes. Then there exist global quantities — energy, linear momentum, angular momentum, Lorentz-boost vector — which are nicely conserved. If those quantities are calculated within Continue reading