arXiv research

New method finds closed timelike geodesics on Lorentzian manifolds.

No closed timelike geodesics in Kerr spacetimes, proving absence of closed causal geodesics.

Some results related to the causality of compact Lorentzian manifolds are proven: (1) any compact Lorentzian manifold which admits a timelike conformal vector field is totally vicious, and (2) a compact Lorentzian manifold covered regularly by a globally hyperbolic spacetime admits a timelike closed geodesic, if some n…

The paper proves uniqueness of closed timelike geodesics on de-Sitter tori with one singularity.

The paper explores conjugate points in Lorentzian spaces, comparing different definitions and proving related theorems.

Study scattering rigidity on stationary manifolds using geodesics.

We study the geometry and the periodic geodesics of a compact Lorentzian manifold that has a Killing vector field which is timelike somewhere. Using a compactness argument for subgroups of the isometry group, we prove the existence of one timelike non self-intersecting periodic geodesic. If the Killing vector field is …

Study of timelike surfaces with time-minimizing rulings in Newtonian and relativistic spacetimes.

Formally constructs metrics near timelike geodesics in vacuum spacetimes.

Geodesics found in spacetime satisfy curvature conditions.

In this paper, by studying certain isometries on globally hyperbolic planes, we prove that if $p$ is a timelike pole on a class A Lorentzian 2-torus, then there exists a closed timelike geodesic passing through $p$ with any preassigned free homotopy class in the interior of the stable time cone. We also show a non-rigi…

The study introduces hyperbolic angles in Lorentzian spaces and characterizes curvature bounds.

New splitting theorem for weighted Finsler spacetimes without Berwald condition.

In this paper, we introduce the dual geodesic trihedron (dual Darboux frame) of a timelike ruled surface. By the aid of the E. Study Mapping, we consider timelike ruled surfaces as dual hyperbolic spherical curves and define the Mannheim offsets of timelike ruled surfaces by means of dual Darboux frame. We obtain the r…

Study of Gödel Universe as Lie group with specific metric.

In this study we give definitions and characterizations of transversal surfaces of timelike ruled surfaces. We study some special cases such as the striction curve is a geodesic, an asymptotic line or a line of curvature. Moreover, we obtain developable conditions for transversal surfaces of a timelike ruled surface.

Study introduces new curvature conditions for Lorentzian spaces using Rényi entropy.

The Sagnac effect is re-examined using Finslerian geometry.

We study homologically maximizing timelike geodesics in conformally flat tori. A causal geodesic $γ$ in such a torus is said to be homologically maximizing if one (hence every) lift of $γ$ to the universal cover is arclength maximizing. First we prove a compactness result for homologically maximizing timelike geodesics…

We show that the index of a lightlike geodesic in a conformally standard stationary spacetime is equal to the index of its spatial projection as a geodesic of a Finsler metric associated to the spacetime. Moreover we obtain the Morse relations of lightlike geodesics connecting a point to an integral line of the standar…

In this study, we investigate the existence theorems for timelike ruled surfaces in Minkowski 3-space. We obtain a general system and give the existence theorems for a timelike ruled surface according to Gaussian curvature, distribution parameter and strictional distance. Moreover, we give some special cases such as th…

Kerr spacetimes without closed null geodesics for non-zero rotation.

The study proves timelike Ricci bounds for low regularity spacetimes using optimal transport.

The paper extends completeness notions to low-regularity spacetimes.

Defines timelike ideal boundary for non-positively curved Lorentzian spaces.

Proves a synthetic Lorentzian Cartan-Hadamard theorem.

Let M be a Margulis spacetime whose associated complete hyperbolic surface S has compact convex core. Generalizing the correspondence between closed geodesics on M and closed geodesics on S, we establish an orbit equivalence between recurrent spacelike geodesics on M and recurrent geodesics on S. In contrast, no timeli…

We show that if $(\mathbb{T}^{2},g)$ is a class A Lorentzian 2-torus with timelike poles, then there exists a Lipschitz foliation by complete future-directed timelike geodesics with any pre-assigned asymptotic direction in the interior of the stable time cone. This is done by constructing certain $C^{1,1}$ solutions to…

Moitvated in part by [3], in this note we obtain a rigidity result for globally hyperbolic vacuum spacetimes in arbitrary dimension that admit a timelike conformal Killing vector field. Specifically, we show that if M is a Ricci flat, timelike geodesically complete spacetime with compact Cauchy surfaces that admits a t…

New research proves uniqueness of maximal spacetime boundaries under certain conditions.

New theorem shows black holes are real, with clearer event horizon.

We construct normal forms for Lorentzian metrics on Engel distributions under the assumption that abnormal curves are timelike future directed Hamiltonian geodesics. Then we indicate some cases in which the abnormal timelike future directed curve initiating at the origin is geometrically optimal. We also give certain e…

Given a Lorentzian manifold $(M,g)$, a geodesic $γ$ in $M$ and a timelike Jacobi field $\mathcal Y$ along $γ$, we introduce a special class of instants along $γ$ that we call $\mathcal Y$-pseudo conjugate (or focal relatively to some initial orthogonal submanifold). We prove that the $\mathcal Y$-pseudo conjugate insta…

This paper deals with the natural lift curves and the geodesic sprays for the spherical indicatrices of the timelike-spacelike Bertrand couple on the tangent bundle or in Minkowski 3-space and then give some new characterizations for these curves. Additionally we illustrate an example of our main results.

Given two points of a Generalized Robertson-Walker spacetime, the existence, multiplicity and causal character of geodesic connecting them is characterized. Conjugate points of such geodesics are related to conjugate points of geodesics on the fiber, and Morse-type relations are obtained. Applications to bidimensional …

We prove that the topology, smooth structure, and metric of a compact Lorentzian manifold with boundary is uniquely determined by data at the boundary. The data consists of the lengths and directions of future-directed once-broken geodesics connecting points on the boundary, which are first timelike and then lightlike.…

Optimizes transport in Finsler spacetimes with lower Ricci bounds.

Study nondifferentiable metrics in general relativity, resolving causality issues and limits evolution scenarios.

We review geometrical properties of a static spacetime $(M,g)$, including geodesic completeness, causality, standard splittings, compact $M$, closed geodesics and geodesic connectedness. We pay special attention to the critical quadratic behavior at infinity of the coefficients $β$, $β^{-1}$ ($β= -g(K,K)$, being $K$ a …

Proves well-posedness for Einstein equations with totally geodesic timelike boundary condition.

Cosmological singularity theorems such as that of Hawking and Penrose assume local curvature conditions as well as global ones like the existence of a compact (achronal) slice. Here, we prove a new singularity theorem for chronological spacetimes that satisfy what we call a `past null focusing' condition. Such a condit…

A celebrated result due to Poincaré affirms that a closed non-degenerate minimizing geodesic $γ$ on an oriented Riemannian surface is hyperbolic. Starting from this classical theorem, our first main result is a general instability criterion for timelike and spacelike closed semi-Riemannian geodesics on a (non)oriented …

The aim of this paper is to determine criteria of being integral curve for the geodesic spray of the natural lift curves of the spherical indicatrices of the involutes of a given spacelike curve with a timelike binormal in Minkowski 3-space. Furthermore, some interesting results about the spacelike evolute curve with t…

In this paper we develop a Morse Theory for timelike geodesics parameterized by a constant multiple of proper time. The results are obtained using an extension to the timelike case of the relativistic Fermat Principle, and techniques from Global Analysis on infinite dimensional manifolds. In the second part of the pape…

We prove Wadsley's theorem for foliations by closed non-lightlike geodesics. As an application we show that every pseudo-Riemannian and non-Riemannian 2-mainfold, all of whose time- or spacelike geodesics are closed, is diffeomorphic to $S^1\times \R$. Further we show that every pseudo-Riemannian 2-manifold with index …

Study timelike Ricci curvature bounds via optimal transport with Orlicz-type costs.

Constructs solutions of Einstein equations for black holes gluing along timelike geodesics.

Causal spacetimes with Ricci tensor have unique transformations.