We describe the local conformal geometry of a Lorentzian spin manifold (M, g) admitting a twistor spinor φ with zero. Moreover, we describe the shape of the zero set of φ. If φ has isolated zeros then the metric g is locally conformally equivalent to a static monopole. In the other case the zero set consists of null geodesic(s) and g is locally conformally equivalent to a Brinkmann metric. Our ...

We recast the tools of " global causal analysis " in accord with an approach to the subject animated by two distinctive features: a thoroughgoing reliance on order-theoretic concepts, and a utilization of the Vietoris topol-ogy for the space of closed subsets of a compact set. We are led to work with a new causal relation which we call K + , and in terms of it we formulate extended definitions ...

De Sitter space-time, essentially our own universe, is plagued by problems at the quantum level. Here we propose that Lorentzian de space-time not fundamental but constitutes only an effective description of a more gravity ground state. This cosmological state graph, appearing on large scales as Riemannian manifold constant negative curvature. We model behaviour matter near this equilibrium Bro...

In this article, we try to understand the mechanisms of the non properness of the action of the group of diffeomorphisms on the space of Lorentzian metrics of a compact manifold. We give a first result that describes the dynamical behavior of the sequences of diffeomorphisms involved which entails the existence of metrics that admit an isotropic geodesic foliation of codimension 1. On the 2-tor...

In 7] the notion of causal compatibility is introduced as a method to determine the conformal structure of space-time uniquely by the net of observable algebras of a quantum eld theory. In this work some new aspects of causal compatibility are discussed. In particular it is shown that for a given lattice of algebras there exists up to conformal equivalence at most one Lorentzian manifold which ...

On a time-oriented Lorentzian manifold (M, g) with non-empty boundary satisfying a convexity assumption, we show that the topological, differentiable, and conformal structure of suitable subsets S ⊂ M of sources is uniquely determined by measurements of the intersection of future light cones from points in S with a fixed open subset of the boundary of M ; here, light rays are reflected at ∂M ac...

In this paper we characterize the convexity of the boundary ∂S of a static (standard) Lorentzian manifold S in terms of Jacobi metrics. From this result, we also obtain: (1) a characterization of the convexity of ∂S computable from its “spacelike” part, (2) the equivalence between the variational and geometrical definitions of convexity for ∂S, and (3) a very precise result on existence of geod...

In a series of papers ([2, 3, 4]) the relations existing between the metric properties of Randers spaces and the conformal geometry of stationary Lorentzian manifolds were discovered and investigated. These relations were called in [4] Stationary-to-Randers Correspondence (SRC). In this paper we focus on one aspect of SRC, the equality between the index of a geodesic in a Randers space and that...

We study the motion of an n-dimensional closed spacelike hypersurface in a Lorentzian manifold in the direction of its past directed normal vector, where the speed equals a positive power p of the mean curvature. We prove that for any p ∈ (0, 1], the flow exists for all time when the Ricci tensor of the ambient space is bounded from below on the set of timelike unit vectors. Moreover, if we ass...

We are concerned with the existence of smooth time functions on connected time–oriented Lorentzian manifolds. The problem is tackled in a more general abstract setting, namely in a manifold M where is just defined a field of tangent convex cones (Cx)x∈M enjoying mild continuity properties. Under some conditions on its integral curves, we will construct a time function. Our approach is based on ...