Classifies left invariant Kundt structures on 3D Lie groups.
problem Understanding Kundt spacetimes and their properties.
method Analyzes local structure and properties of left invariant Kundt structures.
result Classifies all left invariant Kundt structures on 3D simply connected unimodular Lie groups.
Researchers found differential invariants for Kundt spacetimes.
problem Equivalence problem for Lorentzian metrics in Kundt spacetimes.
method Found generators for rational differential invariants for Kundt spacetimes.
result Relating findings to other approaches to the equivalence problem.
Characterizes spacetimes using doubly torqued vectors.
problem Classifying spacetimes based on their geometric properties.
method Characterization through doubly torqued vectors and their properties.
result Doubly twisted and Kundt spacetimes can be characterized.
In this paper we consider a new approach to studying Kundt spacetimes through G-structures. We define a Lie-group GN such that the GN-structures satisfying an integrability condition and an existence criterion, which we call Kundt structures, have the property that each metric belonging to the Kundt structure is …
A pseudo-Riemannian manifold is called CSI if all scalar polynomial invariants constructed from the curvature tensor and its covariant derivatives are constant. In the Lorentzian case, the CSI spacetimes have been studied extensively due to their application to gravity theories. It is conjectured that a CSI spacetime i…
Study isotropic solutions in smooth metric measure spaces with vacuum Einstein equations.
problem Investigate isotropic solutions in smooth metric measure spaces under vacuum Einstein field equations.
method Define a weighted Einstein tensor and associated vacuum field equations. Analyze solutions for different spacetime types.
result Isotropic solutions have nilpotent Ricci operator and specific forms in 2- and 3-step nilpotent manifolds.
We study the existence of a non-spacelike isometry, ζ, in higher dimensional Kundt spacetimes with constant scalar curvature invariants (CSI). We present the particular forms for the null or timelike Killing vectors and a set of constraints for the metric functions in each case. Within the class of N dimensional CSI Ku…
We consider the class of locally boost isotropic spacetimes in arbitrary dimension. For any spacetime with boost isotropy, the corresponding curvature tensor and all of its covariant derivatives must be simultaneously of alignment type D relative to some common null frame. Such spacetimes are known as type ${\b…
Impulsive waves contradict a 1962 conjecture about pp-waves.
problem The failure of the Ehlers--Kundt conjecture in the impulsive case.
method Summarized completeness results for impulsive wave spacetimes.
result Impulsive pp-waves are complete, contradicting the conjecture.
Kundt waves belong to the class of spacetimes which are not distinguished by their scalar curvature invariants. We address the equivalence problem for the metrics in this class via scalar differential invariants with respect to the equivalence pseudo-group of the problem. We compute and finitely represent the algebra o…
We consider restrictions placed by geodesic completeness on spacetimes possessing a null parallel vector field, the so-called Brinkmann spacetimes. This class of spacetimes includes important idealized gravitational wave models in General Relativity, namely the plane-fronted waves with parallel rays, or pp-waves, which…
This paper is concerned with deformations of Kundt metrics in the direction of type III tensors and nil-Killing vector fields whose flows give rise to such deformations. We find various characterizations within the Kundt class in terms of nil-Killing vector fields and obtain a theorem classifying algebraic stability …
Study parallel waves in spacetimes, focusing on causality and open questions.
problem Addressing open questions in the field of parallel waves in spacetimes.
method Review and summarize existing results, introduce new concepts like null coordinates and Penrose limits.
result Progress made on the Ehlers-Kundt conjecture.
It is of interest to study supergravity solutions preserving a non-minimal fraction of supersymmetries. A necessary condition for supersymmetry to be preserved is that the spacetime admits a Killing spinor and hence a null or timelike Killing vector field. Any spacetime admitting a covariantly constant null vector fiel…
Proves the Kundt conjecture in arbitrary dimensions, confirming its validity.
problem Determining spacetimes not characterized by scalar polynomial curvature invariants.
method New bilinear map and analysis of covariant derivatives of the Riemann tensor.
result Confirms the Kundt conjecture in arbitrary dimensions, removing regularity assumptions.
We examine the existence of one parameter groups of diffeomorphisms whose infinitesimal generators annihilate all scalar polynomial curvature invariants through the application of the Lie derivative, known as I-preserving diffeomorphisms. Such mappings are a generalization of isometries and appear to be rel…
We prove a Goldberg-Sachs theorem in dimension three. To be precise, given a three-dimensional Lorentzian manifold satisfying the topological massive gravity equations, we provide necessary and sufficient conditions on the tracefree Ricci tensor for the existence of a null line distribution whose orthogonal complement …
Introduces Kundt spaces using geometric language.
problem Clarify properties of Kundt spaces.
method Geometric approach focusing on key concepts.
result Pedagogical introduction to Kundt spaces.
Berwald geometries are Finsler geometries close to (pseudo)-Riemannian geometries. We establish a simple first order partial differential equation as necessary and sufficient condition, which a given Finsler Lagrangian has to satisfy to be of Berwald type. Applied to (α,β)-Finsler spaces, respectively (A,B)-Finsler…
We discuss the invariant classification of vacuum Kundt waves using the Cartan-Karlhede algorithm, and the upper bound on the number of iterations of the Karlhede algorithm to classify the vacuum Kundt waves. By choosing a particular coordinate system we partially construct the canonical coframe used in the classificat…
We consider weighted parallel spinors in Lorentzian Weyl geometry in arbitrary dimensions, choosing the weight such that the integrability condition for the existence of such a spinor, implies the geometry to be Einstein-Weyl. We then use techniques developed for the classification of supersymmetric solutions to superg…
In this paper we consider pseudo-Riemannian spaces of arbitrary signature for which all of the polynomial curvature invariants vanish (VSI spaces). Using an algebraic classification of pseudo-Riemannian spaces in terms of the boost-weight decomposition we first show more generally that a space which is not characterise…
Study of four-dimensional Lorentzian manifolds with real Killing spinors.
problem Characterizing and understanding four-dimensional Lorentzian manifolds with Killing spinors.
method Differential geometry and topology, Killing spinor equations, flow equations.
result Proves that the evolution flow defined by a real Killing spinor preserves the Hamiltonian and momentum constraints of the Einstein equation with negative curvature.
Study of differential spinors on three-manifolds with skew-torsion.
problem Characterizing differential spinors on Lorentzian three-manifolds with skew-torsion.
method Developed spinorial polyforms and used them to study differential spinors, proving that every differential spinor is equivalent to an isotropic line preserved by a metric connection with skew-torsion.
result Obtained structural results about Lorentzian three-manifolds equipped with skew-torsion parallel spinors, which are necessarily Kundt and geodesically complete in the compact case.
Complete description of flat Lorentzian Lie groups solved.
problem Long-standing open problem in pseudo-Riemannian Lie groups.
method Refined analysis of double extension process and explicit classification of Lie algebras.
result All flat Lorentzian Lie algebras arise from flat Euclidean ones.
Ehlers-Kundt conjecture is a physical assertion about the fundamental role of plane waves for the description of gravitational waves. Mathematically, it becomes equivalent to a problem on the Euclidean plane R2 with a very simple formulation in Classical Mechanics: given a non-necessarily autonomous potent…
We show that every n-dimensional locally homogeneous pp-wave is a plane wave, provided it is indecomposable and its curvature operator, when acting on 2-forms, has rank greater than one. As a consequence we obtain that indecomposable, Ricci-flat locally homogeneous pp-waves are plane waves. This generalises a classic…
Study finds holonomy algebras for Lorentzian Weyl spin manifolds with specific spinors.
problem Characterizing Lorentzian Weyl spin manifolds with weighted parallel spinors.
method Analyzing holonomy algebras and introducing special coordinates.
result Local forms and examples of Lorentzian Weyl spin manifolds with weighted parallel spinors.
The paper finds conditions for pseudosymmetric spacetimes to be perfect fluids.
problem Characterizing pseudosymmetric spacetimes as perfect fluids.
method Analyzes generalized Robertson-Walker spacetimes, conformally flat spacetimes, and dust fluids.
result Conditions for pseudosymmetric spacetimes to be perfect fluids are established.
We consider (flat) Cauchy-complete GH spacetimes, i.e., globally hyperbolic flat lorentzian manifolds admitting some Cauchy hypersurface on which the ambient lorentzian metric restricts as a complete riemannian metric. We define a family of such spacetimes - model spacetimes - including four subfamilies: translation sp…
Jebsen-Birkhoff theorem extended to Berwald spacetimes.
problem Generalizing Birkhoff theorem to Berwald spacetimes.
method Proving Ricci-flat, spatially spherically symmetric Berwald spacetimes are pseudo-Riemannian or flat.
result Jebsen-Birkhoff theorem extended to Berwald spacetimes.
The paper introduces and analyzes pseudo generalized Ricci-recurrent spacetimes in modified gravity.
problem Characterizing and analyzing pseudo generalized Ricci-recurrent spacetimes in modified gravity.
method Introducing and characterizing pseudo generalized Ricci-recurrent spacetimes, proving their properties, and studying their impact under modified gravity scenarios.
result Pseudo generalized Ricci-recurrent spacetimes represent specific spacetime types under modified gravity scenarios.
The study characterizes spacetimes with quasi-constant sectional curvature and explores their properties in F(R)-gravity.
problem Characterizing spacetimes with quasi-constant sectional curvature.
method Investigation through examples, proofs, and analysis of energy conditions.
result A spacetime of quasi-constant sectional curvature can represent a Robertson Walker spacetime or a static spacetime.
The article introduces pseudo generalized Ricci-recurrent spacetimes and their applications in modified gravity.
problem Characterizing and understanding pseudo generalized Ricci-recurrent spacetimes.
method Introduced and characterized pseudo generalized Ricci-recurrent spacetimes, provided examples, and studied their implications in modified gravity.
result Pseudo generalized Ricci-recurrent spacetimes represent perfect fluid spacetimes and can model dark energy epochs or static spacetimes.
The paper studies the past inextendibility of FLRW spacetimes using the VDR asymptote.
problem Investigating the past inextendibility of FLRW spacetimes.
method Using the volume-distance-ratio (VDR) asymptote to assess spacetime inextendibility criteria.
result Conditions for past inextendibility of FLRW spacetimes are identified.
Study explores geometric properties of Vaidya-Bonner-de Sitter spacetime.
problem Exploring geometric properties of Vaidya-Bonner-de Sitter spacetime.
method Analyzing conformal curvature, conharmonic curvature, and other curvatures.
result VBdS spacetime exhibits various pseudosymmetric structures and geometric features.
The study characterizes GRW spacetimes with gradient solitons and phantom era.
problem Characterizing generalized Robertson-Walker spacetimes with gradient solitons.
method Examined gradient type Ricci solitons and (m,τ)-quasi Einstein solitons in GRW spacetimes. result Demonstrated that GRW spacetimes can be Robertson-Walker or phantom era spacetimes under certain conditions.
Characterizes Lorentzian manifolds embeddable in Minkowski spacetime.
problem Identifying Lorentzian manifolds embeddable in Minkowski spacetime.
method Characterization and proof of embeddability conditions.
result Lorentzian manifolds embeddable in Minkowski spacetime coincide with globally hyperbolic spacetimes.
New proof shows FLRW spacetimes can't be extended smoothly in certain axisymmetric cases.
problem Proving smooth extension of FLRW spacetimes in specific spacetime classes.
method Extending previous work on spherically symmetric spacetimes to axisymmetric spacetimes.
result Demonstrates C0-inextendibility for FLRW spacetimes in a subclass of axisymmetric spacetimes. Study of quasilocal mass using isometric embedding in various spacetimes.
problem Understanding quasilocal mass in different spacetimes.
method Application of isometric embedding theory to quasilocal mass.
result Recent progress in quasilocal mass calculations with specific spacetimes.
Characterizes pseudo B-symmetric spacetimes and their implications in f(R) gravity.
problem Characterizing pseudo B-symmetric spacetimes and their properties.
method Analyzes Codazzi type of B-tensor and applies f(R) gravity model.
result Pseudo B-symmetric spacetimes with Codazzi type B-tensor are conformally flat and Robertson-Walker spacetimes.
Characterizes a specific type of spacetime using vector fields.
problem Classifying a specific type of spacetime.
method Using vector fields to characterize 1+n doubly twisted spacetimes.
result Simple classification of 1+n doubly-twisted spacetimes.
Study maximal hypersurfaces in open spacetimes using a maximum principle.
problem Characterize maximal hypersurfaces in open spacetimes.
method Use a generalized maximum principle to analyze hypersurfaces in spatially open Generalized Robertson-Walker spacetimes.
result Provide new uniqueness and non-existence results for complete maximal hypersurfaces in open Robertson-Walker spacetimes.
The study explores properties of a specific type of spacetime.
problem Discussing geometric and physical properties of hyper-generalised quasi-Einstein spacetime.
method Analyzing various types of pseudosymmetry and Ricci symmetry over the spacetime.
result Proved the existence of a non-trivial hyper-generalised quasi-Einstein spacetime.
New findings show cosmological constant as initial condition for non-isotropic spacetimes.
problem Cosmological constant as initial condition in non-isotropic spacetimes.
method Generalized previous results to non-isotropic spacetimes.
result Quasi de Sitter expansion for early universe, potential for inflationary scenarios.
Study finds unique and non-existent constant mean curvature hypersurfaces in specific spacetimes.
problem Finding unique and non-existent constant mean curvature spacelike hypersurfaces.
method Geometric and physical assumptions applied to Generalized Robertson-Walker spacetimes.
result New uniqueness and non-existence results for complete spacelike hypersurfaces.
New Galilean spacetimes found as pp-wave reductions.
problem Understanding isotropic homogeneous Galilean spacetimes.
method Null reductions of pp-wave spacetimes.
result Found novel torsional Galilean spacetimes.
Study revisits Bondi mass and discusses memory effect in polyhomogeneous spacetimes.
problem Analyzing the asymptotic behavior and memory effect in polyhomogeneous spacetimes.
method Revisits Bondi mass using Iyer-Wald formalism and discusses memory effect in vacuum polyhomogeneous spacetimes.
result The balance law remains unchanged in polyhomogeneous spacetimes with logarithmic terms.