Related papers: Maximality and Cauchy developments of Lorentzian l…
The null distance of Sormani and Vega encodes the manifold topology as well as the causality structure of a (smooth) spacetime. We extend this concept to Lorentzian length spaces, the analog of (metric) length spaces, which generalize…
Recently ({\em Class. Quant. Grav.} {\bf 20} 625-664) the concept of {\em causal mapping} between spacetimes --essentially equivalent in this context to the {\em chronological map} one in abstract chronological spaces--, and the related…
It is commonly known that in Riemannian and sub-Riemannian Geometry, the metric tensor on a manifold defines a distance function. In Lorentzian Geometry, instead of a distance function it provides causal relations and the Lorentzian…
The folk questions in Lorentzian Geometry, which concerns the smoothness of time functions and slicings by Cauchy hypersurfaces, are solved by giving simple proofs of: (a) any globally hyperbolic spacetime $(M,g)$ admits a smooth time…
In mathematical modelling, the data and solutions are represented as measurable functions and their quality is oftentimes captured by the membership to a certain function space. One of the core questions for an analysis of a model is the…
We develop a ``canonical Wick rotation-rescaling theory in 3-dimensional gravity''. This includes: (a) A simultaneous classification that shows how generic maximal globally hyperbolic spacetimes of constant curvature, which admit a complete…
A class of elliptic-hyperbolic equations is placed in the context of a geometric variational theory, in which the change of type is viewed as a change in the character of an underlying metric. A fundamental example of a metric which changes…
We determine, for all three-dimensional non-unimodular Lie groups equipped with a Lorentzian metric, the set of homogeneous geodesics through a point. Together with the results of [C] and [CM2], this leads to the full classification of…
We show that the equivalence problem for three-dimensional Lorentzian manifolds requires at most the fifth covariant derivative of the curvature tensor. We prove that this bound is sharp by exhibiting a class of 3D Lorentzian manifolds…
Via a functor from certain Lorentzian to Riemannian manifolds, we obtain a finiteness result.
We establish Gromov's celebrated reconstruction theorem in Lorentzian geometry. Alongside this result, we introduce and study a natural concept of isomorphy of normalized bounded Lorentzian metric measure spaces. We outline applications to…
The 3+1 formulation of scalar-tensor theories of gravity (STT) is obtained in the physical (Jordan) frame departing from the 4+0 covariant field equations. Contrary to the common belief (folklore), the new system of ADM-like equations shows…
We construct a family of closeness functions on the space of finite volume Lorentzian geometries using the abundance of discrete intervals in the underlying random causal sets. Although strictly weaker than a Lorentzian Gromov-Hausdorff…
The emergence of (3+1)-dimensional expanding space-time in the Lorentzian type IIB matrix model is an intriguing phenomenon which was observed in Monte Carlo studies of this model. In particular, this may be taken as a support to the…
The initial value problem is well-defined on a class of spacetimes broader than the globally hyperbolic geometries for which existence and uniqueness theorems are traditionally proved. Simple examples are the time-nonorientable spacetimes…
When optimization theorists consider optimization problems in infinite dimensional spaces, they need to deal with closed convex subsets(usually cones) which mostly have empty interior. These subsets often prevent optimization theorists from…
The constraint equations for smooth $[n+1]$-dimensional (with $n\geq 3$) Riemannian or Lorentzian spaces satisfying the Einstein field equations are considered. It is shown, regardless of the signature of the primary space, that the…
The paper establishes a sharp and rigid isoperimetric-type inequality in Lorentzian signature under the assumption of Ricci curvature bounded below in the timelike directions. The inequality is proved in the high generality of Lorentzian…
A three-dimensional quasi-Fuchsian Lorentzian manifold $M$ is a globally hyperbolic spacetime diffeomorphic to $\Sigma\times (-1,1)$ for a closed orientable surface $\Sigma$ of genus $\geq 2$. It is the quotient $M=\Gamma\backslash…
We consider Lorentzian General Relativity in a cavity with a timelike boundary, with conformal boundary conditions and also a generalization of these boundary conditions. We focus on the linearized gravitational dynamics about the static…