Abrupt Changes in the Multipole Moments of a Gravitating Body

TL;DR

This paper models a sudden change in the multipole moments of a gravitating body, illustrating how such an event can produce observable phenomena like gravitational waves and shells, akin to a supernova.

Contribution

It introduces a model demonstrating abrupt multipole moment changes in a static vacuum spacetime, linking these to gravitational waves and shells, providing insights into astrophysical cataclysms.

Findings

Jump in monopole moment causes dominant stress-energy in the shell.

Jump in quadrupole moment primarily generates gravitational waves.

Model simulates a supernova-like astrophysical event.

Abstract

An example is described in which an asymptotically flat static vacuum Weyl space-time experiences a sudden change across a null hypersurface in the multipole moments of its isolated axially symmetric source. A light-like shell and an impulsive gravitational wave are identified, both having the null hypersurface as history. The stress-energy in the shell is dominated (at large distance from the source) by the jump in the monopole moment (the mass) of the source with the jump in the dipole moment mainly responsible for the stress being anisotropic. The gravitational wave owes its existence prrincipally to the jump in th quadrupole moment of the source confirming what would be expected. This serves as a model of a cataclysmic astrophysical event such as a supernova.