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 the 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 , are referred to as universal cut functions. In particular, one can define from these structures a (complex) centre of mass (and centre 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.