Lorentzian Structures on Branching Spacetimes
David O’Connell
Abstract:
This thesis investigates logical models for branching spacetimes, in the tradition started by Belnap. To get a proper generalization of Minkowski space-time that is closer to physical reality, the thesis adds to Belnap’s causal (i.e. order-theoretic) structure appropriate topological, differentiable and metric structures, and investigates the resulting setting, proving a number of interesting original results. Notably, it is shown that the Minkowskian Branching Spacetimes of Belnap’s school can be seen as non-Hausdorff, time-oriented Lorentzian manifolds in which each history is an open, Lorentzian submanifold isometric to a fixed Minkowski spacetime. The approach used in this thesis naturally lends itself to the construction of a new class of models, which are named Lorentzian Branching Spacetimes. It is shown that these Lorentzian BSTs can be constructed from arbitrary spacetimes, in such a way that many enjoyable causal properties are preserved.