Related papers: Lorentzian length spaces
Metrics structures stemming from the Connes distance promote Moyal planes to the status of quantum metric spaces. We discuss this aspect in the light of recent developments, emphasizing the role of Moyal planes as representative examples of…
The canonical description is based on the prior choice of a spacelike foliation, hence making a reference to a spacetime metric. However, the metric is expected to be a dynamical, fluctuating quantity in quantum gravity. After presenting…
A Lorentzian manifold endowed with a time function, $\tau$, can be converted into a metric space using the null distance, $\hat{d}_\tau$, defined by Sormani and Vega. We show that if the time function is a proper regular cosmological time…
All Lorentzian spacetimes with vanishing invariants constructed from the Riemann tensor and its covariant derivatives are determined. A subclass of the Kundt spacetimes results and we display the corresponding metrics in local coordinates.…
Distance functions of metric spaces with lower curvature bound, by definition, enjoy various metric inequalities; triangle comparison, quadruple comparison and the inequality of Lang-Schroeder-Sturm. The purpose of this paper is to study…
We introduce and solve a family of discrete models of 2D Lorentzian gravity with higher curvature, which possess mutually commuting transfer matrices, and whose spectral parameter interpolates between flat and curved space-times. We further…
We introduce a concept of causality in the framework of generalized pseudo-Riemannian Geometry in the sense of J.F. Colombeau and establish the inverse Cauchy-Schwarz inequality in this context. As an application, we prove a dominant energy…
Some examples from the mathematics of shape are presented that question some of the almost hidden assumptions behind results on limiting behaviour of finitary approximations to space-time. These are presented so as to focus attention on the…
At first we introduce the space-time manifold and we compare some aspects of Riemannian and Lorentzian geometry such as the distance function and the relations between topology and curvature. We then define spinor structures in general…
Penrose's Spin Geometry Theorem is extended further, from $SU(2)$ and $E(3)$ (Euclidean) to $E(1,3)$ (Poincar\'e) invariant elementary quantum mechanical systems. The Lorentzian spatial distance between any two non-parallel timelike…
Feynman's i-epsilon prescription for quantum field theoretic propagators has a quite natural reinterpretation in terms of a slight complex deformation of the Minkowski spacetime metric. Though originally a strictly flat-space result, once…
We present a unified Lorentzian replica-path-integral framework for computing entanglement entropy in fully time-dependent quantum field theories and gravitational systems. Building on this framework, we apply the real-time replica trick to…
We employ the techniques introduced in the companion papers to derive a connection formulation of Lorentzian General Relativity coupled to Dirac fermions in dimensions D+1 > 2 with compact gauge group. The technique that accomplishes that…
We lay down the foundations of particle dynamics in mechanical theories that satisfy the relativity principle and whose kinematics can be formulated employing reference frames of the type usually adopted in special relativity. Such…
We show that many standard results of Lorentzian causality theory remain valid if the regularity of the metric is reduced to $C^{1,1}$. Our approach is based on regularisations of the metric adapted to the causal structure.
We study the question of local and global uniqueness of completions, based on null geodesics, of Lorentzian manifolds. We show local uniqueness of such boundary extensions. We give a necessary and sufficient condition for existence of…
This work is developed in the context of Lorentzian spin-foams with space- and time-like boundaries. It is argued that the equations describing the semiclassical regime of the various spin-foam amplitudes admit a common biquaternionic…
For a Lorentzian space measured by $\mathfrak{m}$ in the sense of Kunzinger, S\"amann, Cavalletti, and Mondino, we introduce and study synthetic notions of timelike lower Ricci curvature bounds by $K\in\boldsymbol{\mathrm{R}}$ and upper…
The theory of gravitational lensing is reviewed from a spacetime perspective, without quasi-Newtonian approximations. More precisely, the review covers all aspects of gravitational lensing where light propagation is described in terms of…
A Riemannian metric on a manifold M induces a family of Riemannian metrics on the loop space LM depending on a Sobolev space parameter s. We compute the connection forms of these metrics and the higher symbols of their curvature forms,…