Study fluid spacetimes, proving shear-free implies vanishing expansion or vorticity.
problem Understanding shear and vorticity in perfect-fluid spacetimes.
method Analyzing perfect-fluid spacetimes using Weyl tensor and divergence.
result Proves shear-free implies vanishing expansion or vorticity for perfect fluids.
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 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.
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.
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 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 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 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.
A generalized Robertson-Walker spacetime is the warped product with base an open interval of the real line endowed with the opposite of its metric and base any Riemannian manifold. The family of generalized Robertson-Walker spacetimes widely extends the one of classical Robertson-Walker spacetimes. In this article we p…
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.
Study harmonicity of metrics in generalized Kantowski-Sachs spacetime.
problem Harmonicity of metrics in generalized Kantowski-Sachs spacetime.
method Considered Sasaki, horizontal and complete lifts of generalized Kantowski-Sachs spacetime metrics to tangent bundle and studied their harmonicity.
result Characterized harmonicity properties of lifted metrics.
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.
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.
Study submanifolds in null hypersurfaces of generalized Robertson-Walker spacetimes.
problem Characterize submanifolds in null hypersurfaces of generalized Robertson-Walker spacetimes.
method Analyze light cones, lightlike cylinders, and null cones in specific spacetimes; provide conditions for conformal diffeomorphism.
result Conditions guaranteeing conformal diffeomorphism to hyperbolic space, round cylinder, and sphere.
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…
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.
Proves mass theorem for spacetimes with irregular curvature.
problem Proving mass theorem for spacetimes with irregular curvature.
method Introduced distributional curvature and generalized ADM momentum.
result Proved Lorentzian positive mass theorem.
The Levi-Civita connection and geodesic equations for a stationary spacetime are studied in depth. General formulae which generalize those for warped products are obtained. These results are applicated to some regions of Kerr spacetime previously studied by using variational methods. We show that they are neither space…
Classifies Lie algebras and related spacetimes for a specific type of symmetry.
problem Classifying Lie algebras and related spacetimes for a specific type of symmetry.
method Classification of Lie algebras, homogeneous spacetimes, and coadjoint orbits.
result Classification of three types of Lifshitz spacetimes.
The higher-dimensional Kerr-NUT-de Sitter spacetime describes the general rotating asymptotically de Sitter black hole with NUT parameters. It is known that such a spacetime possesses a rank-2 closed conformal Killing-Yano (CKY) tensor as a ``hidden'' symmetry which provides the separation of variables for the geodesic…
The study examines Ricci solitons and curvature inheritance on Robinson-Trautman spacetimes.
problem Investigating Ricci solitons and curvature inheritance in Robinson-Trautman spacetimes.
method Analyzing the existence of Ricci solitons and curvature inheritance properties on Robinson-Trautman spacetimes.
result Robinson-Trautman spacetimes admit various types of Ricci solitons and curvature inheritance.
Study on Finsler spacetimes with timelike Killing vectors, introducing stationary splitting.
problem Characterizing Finsler spacetimes with timelike Killing vectors.
method Introducing a new class of stationary splitting Finsler spacetimes and characterizing their properties.
result A Finsler spacetime with a timelike Killing vector field is locally a stationary splitting.
Study Berwald spacetimes and their relation to very special relativity.
problem Understanding vacuum dynamics in Berwald spacetimes.
method Derived Finsler generalization of Einstein's equations and derived conditions for Berwald spacetimes.
result Identified necessary and sufficient conditions for VGR line elements to be Berwald type.
Study characterizes 2-Killing vector fields on complex spacetimes.
problem Characterize 2-Killing vector fields on multiply twisted product spacetimes. method Determine nonlinear differential equations, find twisted functions, provide solutions, and construct examples.
result Completely describe 2-Killing vector fields and twisted functions on multiply twisted product spacetimes. New rigidity results for specific hypersurfaces in spacetimes.
problem Characterizing maximal hypersurfaces in Generalized Robertson-Walker spacetimes.
method Applying rigidity results under geometric assumptions and the Null Energy Condition.
result New parametric uniqueness and nonexistence results for maximal hypersurfaces.
The paper solves a curvature equation for a specific spacetime foliation.
problem Characterizing foliations in a Generalized Robertson-Walker spacetime.
method Analyzing a mean curvature equation on spacelike graphs.
result All entire solutions of the curvature equation are found.
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.
Mathematical framework for field theories on Finsler spacetimes.
problem Developing a consistent calculus for field theories on Finsler spacetimes.
method Constructing configuration bundles and applying coordinate-free calculus of variations.
result Averaged energy-momentum conservation law for Finsler field theories.
Study examines solutions to Jang equation on anti-de Sitter spacetimes.
problem Existence and properties of solutions to the generalized Jang equation.
method Rigorous analysis in asymptotically anti-de Sitter setting.
result Provides solutions for a broad class of asymptotic conditions.
Study on trapped submanifolds in spacetimes, proving rigidity and non-existence results.
problem Rigidity and non-existence of trapped submanifolds in spacetimes.
method Analysis of parabolic spacelike submanifolds with causal mean curvature in orthogonally splitted and globally hyperbolic spacetimes.
result Non-existence of local minima or maxima of certain functions on submanifolds, leading to rigidity results.
We formulate the concept of time machine structure for spacetimes exhibiting a compactely constructed region with closed timelike curves. After reviewing essential properties of the pseudo Schwarzschild spacetime introduced by A. Ori, we present an analysis of its geodesics analogous to the one conducted in the case of…
Generic singularities found in spacetimes with weakly trapped submanifolds.
problem Existence of singularities in spacetimes with weakly trapped submanifolds.
method Using Whitney topologies and singularity theorems, the study shows genericity of singularities in spacetimes with weakly trapped submanifolds.
result Generic singularities are found in spacetimes with weakly trapped submanifolds.
The paper extends an Alexandrov theorem to Minkowski spacetime.
problem Generalizing Alexandrov's theorem to Minkowski spacetime.
method Adapting conditions for closed codimension-two spacelike submanifolds in Minkowski spacetime.
result A generalized Alexandrov theorem for Minkowski spacetime.
Study on spacelike submanifolds in generalized Schwarzschild spacetimes with lightlike foliations.
problem Characterizing spacelike submanifolds in generalized Schwarzschild spacetimes.
method Analyzing submanifolds under lightlike foliations and using explicit formulas for mean curvature.
result Derived characterizations of slices and specific cases like Schwarzschild and Reissner-Nordström spacetimes.
The study examines perfect fluid spacetimes and their properties.
problem Characterizing properties of perfect fluid spacetimes with concircular vector fields.
method Analyzing the conformal curvature tensor, state equation, and solitons in perfect fluid spacetimes.
result Perfect fluid spacetimes with concircular vector fields have specific properties related to the state equation and solitons.
Researchers generalize cosmological models using Finsler geometry.
problem Cosmological models that closely approximate pseudo-Riemannian geometry.
method Identifying Lie Algebra of symmetry generators for spatially homogeneous and isotropic Finsler geometries.
result Found the most general spatially homogeneous and isotropic Berwald spacetimes.
Study geometric properties and physical applications of mixed quasi-Einstein spacetime.
problem Characterize geometric and physical properties of mixed quasi-Einstein spacetime.
method Analyze geometric conditions and curvature tensors on mixed quasi-Einstein and nearly quasi-Einstein manifolds.
result Establish conditions for specific curvature tensors and spacetime structures.
Paper defines semi-quasi-Einstein manifolds and applies to Schwarzschild and Kottler spacetimes.
problem Defining and studying semi-quasi-Einstein manifolds.
method Introduced from a semi symmetric metric connection, analyzed with curvature conditions and Killing generators.
result Schwarzschild and Kottler spacetimes exhibit semi-quasi-Einstein structure.
Together with collaborators, we introduced a noncommutative Riemannian geometry over Moyal algebras and systematically developed it for noncommutative spaces embedded in higher dimensions in the last few years. The theory was applied to construct a noncommutative version of general relativity, which is expected to capt…
New rigidity results for submanifolds in GRW spacetimes.
problem Characterizing submanifolds in GRW spacetimes.
method Maximum principles and rigidity results.
result Submanifolds must be contained in a spacelike slice.
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.
The paper examines gravitational singularities in spacetimes and proves inextendibility.
problem Investigating gravitational singularities in spacetimes.
method Analyzing local holonomy and using it to prove inextendibility.
result Proves the Cloc0,1-inextendibility of certain spacetimes. Study generalizes submetry concept for spacetimes, linking to curvature and foliations.
problem Understanding submetry in non-positive signature spacetimes.
method Developed Lorentzian submetries and established their equivalence to semi-Riemannian submersions.
result Lorentzian submetries correspond to locally C^{1,1} semi-Riemannian submersions under completeness assumptions.
The paper examines curvature properties of charged Nariai spacetimes.
problem Investigating geometric structures of charged Nariai spacetimes.
method Analyzing curvature properties and geometric structures of charged Nariai spacetimes.
result Charged Nariai spacetimes are locally symmetric, 2-quasi-Einstein, and Ein(2)-space.
The `observer space' of a Lorentzian spacetime is the space of future-timelike unit tangent vectors. Using Cartan geometry, we first study the structure a given spacetime induces on its observer space, then use this to define abstract observer space geometries for which no underlying spacetime is assumed. We propose ta…
Revisits Finsler spacetimes from inertial observer perspective.
problem Physical foundations of relativistic spacetimes.
method Inertial observers and double linear approximation.
result Finsler spacetimes are defined by dropping the second linearization.
The paper discusses when spacetimes have constant mean curvature slices, an important but unknown condition.
problem The existence of constant mean curvature (CMC) Cauchy surfaces in spacetimes is crucial but not always guaranteed.
method Expository review of existing results and conjectures about CMC slices in spacetimes.
result It is not known whether spacetimes with CMC slices are generic, highlighting an important open problem.
Som-Raychaudhuri spacetime is a stationary cylindrical symmetric solution of Einstein field equation corresponding to a charged dust distribution in rigid rotation. The main object of the present paper is to investigate the curvature restricted geometric structures admitting by the Som-Raychaudhuri spacetime and it is …