ﻻ يوجد ملخص باللغة العربية
This chapter is an up-to-date account of results on globally hyperbolic spacetimes, and serves several purposes. We begin with the exposition of results from a foundational level, where the main tools are order theory and general topology, we continue with results of a more geometric nature, and we conclude with results that are related to current research in theoretical physics. In each case, we list a number of open questions and formulate, for a class of spacetimes, an interesting connection between global hyperbolicity of a manifold and the geodesic completeness of its corresponding space-like surfaces. This connection is substantial for the proof of essential self-adjointness of a class of pseudo differential operators, that stem from relativistic quantum field theory.
We show that maximal causal curves for a Lipschitz continuous Lorentzian metric admit a $mathcal{C}^{1,1}$-parametrization and that they solve the geodesic equation in the sense of Filippov in this parametrization. Our proof shows that maximal causal
A systematic study of (smooth, strong) cone structures $C$ and Lorentz-Finsler metrics $L$ is carried out. As a link between both notions, cone triples $(Omega,T, F)$, where $Omega$ (resp. $T$) is a 1-form (resp. vector field) with $Omega(T)equiv 1$
A spinless covariant field $phi$ on Minkowski spacetime $M^{d+1}$ obeys the relation $U(a,Lambda)phi(x)U(a,Lambda)^{-1}=phi(Lambda x+a)$ where $(a,Lambda)$ is an element of the Poincare group $Pg$ and $U:(a,Lambda)to U(a,Lambda)$ is its unitary repre
In this paper, we examine the relationship between general relativity and the theory of Einstein algebras. We show that according to a formal criterion for theoretical equivalence recently proposed by Halvorson (2012, 2015) and Weatherall (2015), the two are equivalent theories.
We use planar coordinates as well as hyperbolic coordinates to separate the de Sitter spacetime into two parts. These two ways of cutting the de Sitter give rise to two different spatial infinities. For spacetimes which are asymptotic to either half