arXiv research

Diagonalizes metrics of 3D Lorentzian manifolds.

Continuous Lorentzian metrics yield infinitesimal Minkowskian spacetimes.

Defines new metrics for Lorentzian spaces and their convergence.

Study left-invariant Codazzi tensors and harmonic curvature on Lorentzian Lie groups.

We consider Lie groups equipped with a left-invariant cyclic Lorentzian metric. As in the Riemannian case, in terms of homogeneous structures, such metrics can be considered as different as possible from bi-invariant metrics. We show that several results concerning cyclic Riemannian metrics do not extend to their Loren…

New concept of Lorentzian-Euclidean black holes and metric transitions explored.

Study left invariant Lorentzian metrics on 3D non-unimodular Lie groups.

Defines metrics for Lorentzian spaces and explores maximal developments.

Study recovers Lorentzian metrics from boundary data, proving local rigidity.

New connections found with specific torsion properties.

The paper reconstructs Lorentzian spacetimes from causal sets.

Researchers extend the concept of metric spaces to Lorentzian spaces and prove the feasibility of their c-completion.

The b-boundary is a mathematical tool used to attach a topological boundary to incomplete Lorentzian manifolds using a Riemaniann metric called the Schmidt metric on the frame bundle. In this paper, we give the general form of the Schmidt metric in the case of Lorentzian surfaces. Furthermore, we write the Ricci scalar…

Formula for sectional curvature on 2D Lorentzian manifolds derived.

Study properties of semi-symmetric Lorentzian spaces, foliated manifolds.

Study the metric geometry of Cauchy hypersurfaces in spacetimes.

In this paper, a survey of the recent results about the classification of the connected holonomy groups of the Lorentzian manifolds is given. A simplification of the construction of the Lorentzian metrics with all possible connected holonomy groups is obtained. As the applications, the Einstein equation, Lorentzian man…

Optimal transport explored on a specific geometric space.

New metrics constructed dual to specific wave-like geometries.

Researchers find counterexamples to inverse problems for wave equations.

The study finds obstructions to certain Riemannian metrics using Lorentzian geometry.

Formula derived for curvature on smooth manifolds.

The study constructs a Lorentzian length space and explores its properties and relationships with metric and causal geometry.

Study on recovering Lorentzian metrics from scattering data.

Proves limit curve theorem for incomplete metric spaces, applies to null distance in Lorentzian manifolds.

New conformally Einstein metrics on Heisenberg group found.

Characterizes intrinsic Lorentzian spaces using midpoint properties.

We present a systematic study of causality theory on Lorentzian manifolds with continuous metrics. Examples are given which show that some standard facts in smooth Lorentzian geometry, such as light-cones being hypersurfaces, are wrong when metrics which are merely continuous are considered. We show that existence of t…

Local Lorentzian theorem preserves metrics or makes them flat.

Synthetic approach to conformal transformations in metric and Lorentzian spaces.

The paper constructs Gromov-Hausdorff metrics for Lorentzian spaces and calculates dimensions.

In this paper, we study Lorentzian left invariant Einstein metrics on nilpotent Lie groups. We show that if the center of such Lie groups is degenerate then they are Ricci-flat and their Lie algebras can be obtained by the double extension process from an abelian Euclidean Lie algebra. We show that all nilpotent Lie gr…

We describe the structure of $d$-dimensional homogeneous Lorentzian $G$-manifolds $M=G/H$ of a semisimple Lie group $G$. Due to a result by N. Kowalsky, it is sufficient to consider the case when the group $G$ acts properly, that is the stabilizer $H$ is compact. Then any homogeneous space $G/\bar H$ with a smaller gro…

We investigate connections between pairs of (pseudo-)Riemannian metrics whose sum is a (tensor) product of a covector field with itself. A bijective mapping between the classes of Euclidean and Lorentzian metrics is constructed as a special result. The existence of such maps on a differentiable manifold is discussed. S…

Study magnetic perturbations in Riemannian and Lorentzian Calderón problems.

The paper classifies tensors on specific Lorentzian metrics.

A Lorentzian flat Lie group is a Lie group $G$ with a flat left invariant metric $μ$ with signature $(1,n-1)=(-,+,\ldots,+)$. The Lie algebra $\mathfrak{g}=T_eG$ of $G$ endowed with $\langle\;,\;\rangle=μ(e)$ is called flat Lorentzian Lie algebra. It is known that the metric of a flat Lorentzian Lie group is geodesical…

We determine all Ricci flat left invariant Lorentzian metrics on simply connected 2-step nilpotent Lie groups. We show that the $2k+1$-dimensional Heisenberg Lie group $H_{2k+1}$ carries a Ricci flat left invariant Lorentzian metric if and only if $k=1$. We show also that for any $2\leq q\leq k$, $H_{2k+1}$ carries a R…

New method glues Lorentzian spaces, preserving curvature bounds.

All candidates to the weakly-irreducible not irreducible holonomy algebras of Lorentzian manifolds are known. In the present paper metrics that realize all these candidates as holonomy algebras are given. This completes the classification of the Lorentzian holonomy algebras. Also new examples of metrics with the holono…

The paper classifies metrics on specific Lie groups and finds unique properties of these metrics.

Researchers solve a formally determined inverse problem in Lorentzian geometry.

Study classifies Einstein-Yang-Mills spaces in 4D symmetric spaces.

Study on special Lie groups with Lorentzian metrics.

Maximal causal curves for Lipschitz metrics are either lightlike or timelike.

Researchers generalize space forms in Riemannian geometry using specific vector fields.

The maximal analytic Schwarzschild spacetime is manifestly inextendible as a Lorentzian manifold with a twice continuously differentiable metric. In this paper, we prove the stronger statement that it is even inextendible as a Lorentzian manifold with a continuous metric. To capture the obstruction to continuous extens…

The local classification of conformally flat Lorentzian manifolds with special holonomy groups is obtained. The corresponding local metrics are certain extensions of Riemannian spaces of constant sectional curvature to Walker metrics.