Dual-mass in general relativity

Abstract

A general notion of dual-mass, the gravitational analog of the magnetic monopole, is formulated in space-times that are asymptotically empty and flat at null infinity and in which the Bondi news vanishes. Dual-mass is specified by a real valued linear function on the asymptotic infinitesimal translation symmetries which, furthermore, depends on the asymptotic dual Weyl curvature tensor. It is shown that space-times with nonzero dual-mass are characterized by a null boundary (null infinity) having the structure of a principal S¹ fiber bundle over S² such that the dual-mass is proportional to the number of twists, n, in the bundle. Thus the topology of null infinity is that of a lens space L(n,1). A consequence of the existence of dual-mass is that the space-time is acausal. The NUT space-time is shown to be an example exhibiting these features, with a null infinity having the three-sphere topology.