University of Pittsburgh

A major issue in general relativity, from its earliest days to the

present, is how to extract physical information from any solution or

class of solutions to the Einstein equations. Though certain

information can be obtained for arbitrary solutions, e.g., via geodesic

deviation, in general, because of the coordinate freedom, it is often

hard or impossible to do. Most of the time information is found from

special conditions, e.g., degenerate principle null vectors, weak

fields close to Minkowski space (using coordinates close to Minkowski

coordinates) or from solutions that have symmetries or approximate

symmetries. In the present work we will be concerned with

asymptotically flat space times where the approximate symmetry is the

Bondi-Metzner-Sachs (BMS) group. For these spaces the Bondi

four-momentum vector and its evolution, found from the Weyl tensor at

infinity, describes the total energy-momentum of the interior source

and the energy-momentum radiated. By generalizing certain structures

from algebraically special metrics, by generalizing the Kerr and the

charged-Kerr metric and finally by defining (at null infinity) the

complex center of mass (the real center of mass plus 'i' times the

angular momentum) with its transformation properties, a large variety

of physical identifications can be made. These include an auxiliary

Minkowski space viewed from infinity, kinematic meaning to the Bondi

momentum, dynamical equations of motion for the center of mass, a

geometrically defined spin angular momentum and a conservation law with

flux for total angular momentum.