Existence and observability of spinor structure Available to Purchase

A mechanism by which space‐time topological modifications could have been controlled, in the early universe or at the Planck length, to enable onset of spinor structure is investigated. This mechanism (based on a reshuffling of topological charges and related modification of characteristic classes) could provide a gravitational analog of the Aharonov–Susskind Gedankenexperiment proposed to detect relative rotation in the universe, spinor behavior, or to keep track of the two homotopy classes of the Lorentz Lie group. The space‐time topology [and in particular the trivial (nontrivial) bundle structure at conformal null infinity] provide a labeling of the asymptotic Lorentz homotopy classes which originates in the first Chern class (enclosed magnetic mass) or in the parametrization of the second homology group, and gives rise to a necessary (and sufficient) condition for the existence of spinor structure. This underlines the intertwined roles of topology and curvature. The mechanism could also be viewed as an ‘‘unwinding’’ of gravitational magnetic monopoles with one asymptotic region into electric mass (black‐hole) solutions with two asymptotic regions. In such situations a discrete PT symmetry could emerge from a continous transformation. Possible implications on the CPT theorem are mentioned.