The theory of gravitational lensing is reviewed from a spacetime perspective, without quasi-
Newtonian approximations. More precisely, the review covers all aspects of gravitational …

We review the first modern singularity theorem, published by Penrose in 1965. This is the
first genuine post-Einsteinian result in general relativity, where the fundamental and fruitful …

The Cauchy slicings for globally hyperbolic spacetimes and their relation with the causal
boundary are surveyed and revisited, starting at the seminal conformal boundary …

Causality is an essential specific tool of Lorentzian geometry, which appears as a fruitful
interplay between relativistic motivations and geometric developments. Most of the goals of …

Within this chapter we introduce the overall idea of the algebraic formalism of QFT on a fixed
globally hyperbolic spacetime in the framework of unital*-algebras. We point out some …

Green-hyperbolic operators are linear differential operators acting on sections of a vector
bundle over a Lorentzian manifold which possess advanced and retarded Green's …

In general relativity, time functions are crucial objects whose existence and properties are
intimately tied to the causal structure of a spacetime and also to the initial value formulation …

We consider the question of future global non-linear stability in the case of Einstein's
equations coupled to a non-linear scalar field. The class of potentials V to which our results …

In this article, we provide notes that complement the lectures on the relativistic Euler
equations and shocks that were given by the second author at the program Mathematical …

Given any half-sided modular inclusion of standard subspaces, we show that the entropy
function associated with the decreasing one-parameter family of translated standard …