4 research outputs found
Charge and the topology of spacetime
A new class of electrically charged wormholes is described in which the outer 2-sphere is not spanned by a compact, co-orientable hypersurface, These wormholes can therefore display net electric charge from the source-free Maxwell equations. This extends the work of Sorkin on non-space-orientable manifolds, to spacetimes which do not admit a time orientation. The work is motivated by the suggestion that quantum theory can be explained by modelling elementary particles as regions of spacetime with non-trivial causal structure. The simplest example of an electrically charged spacetime carries a spherical symmetry
Ricci-corrected derivatives and invariant differential operators
We introduce the notion of Ricci-corrected differentiation in parabolic
geometry, which is a modification of covariant differentiation with better
transformation properties. This enables us to simplify the explicit formulae
for standard invariant operators given in work of Cap, Slovak and Soucek, and
at the same time extend these formulae from the context of AHS structures
(which include conformal and projective structures) to the more general class
of all parabolic structures (including CR structures).Comment: Substantially revised, shortened and simplified, with new treatment
of Weyl structures; 24 page