The Universal Cut Function and Type II Metrics

Abstract

In analogy with classical electromagnetic theory, where one determines the total charge and both electric and magnetic multipole moments of a source from certain surface integrals of the asymptotic (or far) fields, it has been known for many years - from the work of Hermann Bondi - that energy and momentum of gravitational sources could be determined by similar integrals of the asymptotic Weyl tensor. Recently we observed that there were certain overlooked structures, {defined at future null infinity,} that allowed one to determine (or define) further properties of both electromagnetic and gravitating sources. These structures, families of {complex} `slices' or `cuts' of Penrose's null infinity, are referred to as Universal Cut Functions, (UCF). In particular, one can define from these structures a (complex) center of mass (and center of charge) and its equations of motion - with rather surprising consequences. It appears as if these asymptotic structures contain in their imaginary part, a well defined total spin-angular momentum of the source. We apply these ideas to the type II algebraically special metrics, both twisting and twist-free.

32 pages

References in corpus (1)

• On the Physical Meaning of the Robinson-Trautman-Maxwell Fields

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• Vacuum non-expanding horizons and shear-free null geodesic congruences
• Electromagnetic Induced Gravitational Perturbations
• The Gravitational Field of a Radiating Electromagnetic Dipole
• Newton's 2nd Law, Radiation Reaction & Type II Einstein-Maxwell Fields