## On Extracting Physical Content from Asymptotically Flat Space-Time Metrics

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Kozameh, C.

Newman, E. T.

Silva-Ortigoza, G.

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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 the
structures (shear-free null geodesic congruences) associated with the
algebraically special metrics to asymptotically shear-free null geodesic
congruences, which are available in all asymptotically flat 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 geometric meaning.
Among other items, from dynamic arguments, we define 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 flux.

Comment: 33 pages

Comment: 33 pages

##### Keywords

General Relativity and Quantum Cosmology