On Extracting Physical Content from Asymptotically Flat Space-Time Metrics

C. KOZAMEH, E. T. NEWMAN, G. SILVA-ORTIGOZA

CLASSICAL AND QUANTUM GRAVITY

IOP Publishing

Lugar: Londres; Año: 2008 vol. 25 p. 145001 - 145028

0264-9381

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 so- lutions 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., de- generate principle null vectors, weak ¯elds close to Minkowski space (us- ing coordinates close to Minkowski coordinates) or from solutions that have symmetries or approximate symmetries. In the present work we will be concerned with asymptotically °at space times where the approx- imate 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 in¯nity, describes the total energy-momentum of the interior source and the energy-momentum radiated. By generalizing the structures (shear-free null geodesic congruences) associated with the al- gebraically special metrics to asymptotically shear-free null geodesic con- gruences, which are available in all asymptotically °at space-times, we give kinematic meaning to the Bondi four-momentum. In other words we describe the Bondi vector and its evolution in terms of a center of mass position vector, its velocity and a spin-vector, all having clear geo- metric meaning. Among other items, from dynamic arguments, we de¯ne a unique (at our level of approximation) total angular momentum and extract its evolution equation in the form of a conservation law with an angular momentum °ux. extract its evolution equation in the form of a conservation law with an angular momentum °ux. extract its evolution equation in the form of a conservation law with an angular momentum °ux. our level of approximation) total angular momentum and extract its evolution equation in the form of a conservation law with an angular momentum °ux.