Ettore Minguzzi

The causal hierarchy of spacetimes

The Einstein universe is the conformal compactification of Minkowski space. It also arises as the ideal boundary of anti-de Sitter space. The purpose of this article is to develop the synthetic geometry of the Einstein universe in terms of its homogeneous submanifolds and causal structure, with particular emphasis on dimension 2+1, in which there is a rich interplay with symplectic geometry.This is a survey about conformal mappings between pseudo-Riemannian manifolds and, in particular, conformal vector fields defined on such. Mathematics Subject Classification (2000). Primary 53C50; Secondary 53A30; 83C20.We study the geometry of type II supergravity compactifications in terms of an oriented vector bundle

K-Causality Coincides with Stable Causality

E

Chronological Spacetimes without Lightlike Lines are Stably Causal

, endowed with a bundle metric of split signature and further datum. The geometric structure is associated with a so-called generalised

Light Cones in Finsler Spacetime

G

Time Functions as Utilities

-structure and characterised by an

Normally Preordered Spaces and Utilities

E

On differentiability of volume time functions

-spinor

Possible relation between galactic flat rotational curves and the Pioneers’ anomalous acceleration

\rho

Characterization of some causality conditions through the continuity of the Lorentzian distance

, which we can regard as a differential form of mixed degree. This enables us to reformulate the field equations of type II supergravity as an integrability condition of type

Area Theorem and Smoothness of Compact Cauchy Horizons

d_H\rho=0