Global techniques, dual mass, and causality violation

Abstract

A mathematical framework is presented for the description of (magnetic) monopoles or their gravitational analogs. Using Penrose’s global techniques, a proof of a theorem to the effect that, for vacuum space-times with wormhole and an everywhere timelike and complete Killing vector field, the topology must be that of a principal S1 fiber bundle over S2×R (topology of the manifold of orbits of the stationary Killing vector field) if the dual mass (the gravitational analog of the magnetic monopole) does not vanish, is presented. Hence the presence of this magnetic charge induces a causality violation: it is shown that it measures the number of windings of the space-time bundle around its fiber, or the periodicity of the timelike closed loops. If, in addition, the manifold of orbits of the stationary Killing field is asymptotically flat, or if a rotational Killing field is present, the resulting expressions of the dual mass reinsure the fact that it should be viewed as a monopole source of angular momentum. The NUT solution is presented as an example of space-time exhibiting the above features. The role of dual mass solutions in quantum gravity is considered.