Related papers: Observations and predictions from past lightcones

The LHC will probe the nature of the vacuum that determines the properties of particles and the forces between them. Of particular importance is the fact that our current theories allow the Universe to be trapped in a metastable vacuum,…

We consider the relation between the c-completion of a Lorentz manifold V and its quotient M = V/G, where G is an isometry group acting freely and properly discontinuously. First, we consider the future causal completion case,…

The prospect of identifying wormholes by investigating the shadows of wormholes constitute a foremost source of insight into the evolution of compact objects and it is one of the essential problems in contemporary astrophysics. The nature…

We prove that if $M$ is a strictly stable complete minimal hypersurface in Euclidean space with finite density at infinity and which lies on one side of a minimal cylinder with cross-section a strictly stable area minimizing hypercone, then…

Because no closed timelike curve (CTC) on a Lorentzian manifold can be deformed to a point, any such manifold containing a CTC must have a topological feature, to be called a timelike wormhole, that prevents the CTC from being deformed to a…

For a Riemannian manifold $(M,g)$ with strictly convex boundary $\partial M$, the lens data consists in the set of lengths of geodesics $\gamma$ with endpoints on $\partial M$, together with their endpoints $(x_-,x_+)\in \partial M\times…

The geodesic-light-cone (GLC) coordinates are a useful tool to analyse light propagation and observations in cosmological models. In this article, we propose a detailed, pedagogical, and rigorous introduction to this coordinate system,…

It is proved that every compactly generated future Cauchy horizon has past complete generators, and dually. No condition on the differentiability of the horizon is imposed.

Motivated by recent work of Choquet-Bruhat, Chrusciel, and Martin-Garcia, we prove monotonicity properties and comparison results for the area of slices of the null cone of a point in a Lorentzian manifold. We also prove volume comparison…

We prove that any smooth vacuum spacetime containing a compact Cauchy horizon with surface gravity that can be normalised to a non-zero constant admits a Killing vector field. This proves a conjecture by Moncrief and Isenberg from 1983…

There are two versions of the dominant energy condition (=dec): The original one for Lorentzian manifolds and an associated one for initial data sets. If a Lorentzian manifold satisfies dec, then so does the induced initial set on any…

In this short note we argue that, even if, as sometimes remarked, a Lorentzian manifold does not model correctly the structure of the spatio-temporal continuum as it is, yet a Lorentzian manifold should describe its macroscopic structure as…

Continuing work initiated in an earlier publication [Phys. Rev. D 69, 084007 (2004)], we construct a system of light-cone coordinates based at a geodesic world line of an arbitrary curved spacetime. The construction involves (i) an…

Let $M$ be an orientable surface immersed in the De Sitter space $S_1^3$ in $R^4_1$ or anti de Sitter space $H_1^3$ in $R^4_2$. In the case that $M$ is of $L_1$-2-type we prove that the following conditions are equivalent to each other: $M$…

Supersymmetric solutions of supergravity theories, and consequently metrics with special holonomy, have played an important role in the development of string theory. We describe how a Lorentzian manifold is either completely reducible, and…

Chernov-Nemirovski observed that the existence of a globally hyperbolic Lorentzian metric on a (3 + 1)-spacetime pins down a smooth structure on the underlying 4-manifold. In this paper, we point out that the diffeomorphism type of a…

Decaying vacuum models are a class of models that incorporate the vacuum energy density as a time-evolving entity that has the potential to explain the entire evolutionary history of the universe in a single framework. A general solution to…

In this paper, we show that ``$L$-complete null hypersurfaces'' (i.e. ruled hypersurfaces foliated by entirety of light-like lines) as wave fronts in the $(n+1)$-dimensional Lorentz-Minkowski space are canonically induced by hypersurfaces…

With several concrete examples of zero mean curvature surfaces in $\boldsymbol{R}^3_1$ containing a light-like line recently having been found, here we construct all real analytic germs of zero mean curvature surfaces by applying the…

The global characteristic initial value problem for linear wave equations on globally hyperbolic Lorentzian manifolds is examined, for a class of smooth initial value hypersurfaces satisfying favourable global properties. First it is shown…