The Universal Cut Function and Type II Metrics

TL;DR

This paper introduces the Universal Cut Function (UCF) framework at null infinity, enabling new definitions of source properties like center of mass and spin, with applications to type II algebraically special metrics.

Contribution

It develops the concept of UCFs at null infinity to define source characteristics and explores their implications for gravitational and electromagnetic sources.

Findings

UCFs allow defining complex center of mass and spin from asymptotic structures.

Imaginary parts of UCFs relate to total spin-angular momentum.

Application to type II metrics demonstrates the framework's utility.

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.