We study real linear scalar eld theory on two simple non-globally hyperbolic spacetimes containing closed timelike curves within the framework proposed by Kay for algebraic quantum eld theory on non-globally hyperbolic spacetimes. In this context, a spacetime (M; g) is said to be `F-quantum compatible' with a eld theory if it admits a -algebra of local observables for that theory which satis es...

Space-time is spherically symmetric if it admits the group of SO(3) as a group of isometries, with the group orbits spacelike two-surfaces. These orbits are necessarily two-surface of constant positive curvature. One commonly chooses coordinate {t, r, θ, φ} so that the group orbits become surfaces {t, r = const} and the radial coordinate r is defined by the requirement that 4πr is the area of t...

Let $${{\mathcal {H}}}$$ denote the future outgoing null hypersurface emanating from a spacelike 2-sphere S in vacuum spacetime $$({{\mathcal {M}}},\textbf{g})$$ . In this paper we study so-called canonical foliation on introduced [13, 22] and show that corresponding geometry is controlled locally only terms of initial $$L^2$$ curvature flux through particular, ingoing expansions $${\textrm{tr}...

A method is presented for imputing a topology for any chronological set, i.e., a set with a chronology relation, such as a spacetime or a spacetime with some sort of boundary. This topology is shown to have several good properties, such as replicating the manifold topology for a spacetime and replicating the expected topology for some simple examples of spacetime-with-boundary; it also allows f...

The existence of a singularity by definition implies a preferred scale—the affine parameter distance from/to the singularity of a causal geodesic that is used to define it. However, this variable scale is also captured by the expansion along the geodesic, and this can be used to obtain a regularized state space picture by means of a conformal transformation that factors out the expansion. This ...

Recently, a type of null experiment for spacelike neutrinos has been proposed. We examine in detail a class of null tests involving nuclear beta decay or capture in atoms and ions. The most promising candidate systems are identified.