Dual-mass in general relativity

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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.

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