Maximal hypersurfaces in spacetimes with translational symmetry are characterized and their properties studied.
problem Characterizing maximal hypersurfaces in spacetimes with translational symmetry.
method Analyzing quotient spacetimes and using properties of maximal hypersurfaces.
result Complete noncompact maximal hypersurfaces in quotient spacetimes are either cylinders or conformal to the Euclidean plane.
The paper classifies coverings and non-Hausdorff extensions of Misner spacetime.
problem Classifying coverings and non-Hausdorff extensions of Misner spacetime.
method Covering constructions of the punctured Minkowski plane, quotient spacetimes, and explicit embeddings.
result A natural family of spacetimes including the Hawking--Ellis extension and its universal-cover analogue.
Affine deformations of convex cones yield special spacetime structures.
problem Deforming divisible convex cones in affine spaces.
method Analyzing the maximal convex domains and quotient structures.
result Quotients of affine actions are MGHCC affine spacetimes.
This study explores Kaluza-Klein reductions of new maximally supersymmetric backgrounds.
problem Exploring new maximally supersymmetric backgrounds in five dimensions.
method Classifying Kaluza-Klein reductions to four dimensions and determining preserved supersymmetry.
result Discovery of novel non-homogeneous four-dimensional Lorentzian spacetimes with N=1 supersymmetry. We show that Margulis spacetimes without parabolic holonomy are topologically tame. A Margulis spacetime is the quotient of the 3-dimensional Minkowski space by a free proper isometric action of the free group of rank ≥2. We will use our particular point of view that the Margulis spacetime is a manifold-with-bo…
Starting from the recent classification of quotients of Freund--Rubin backgrounds in string theory of the type AdS_{p+1} x S^q by one-parameter subgroups of isometries, we investigate the physical interpretation of the associated quotients by discrete cyclic subgroups. We establish which quotients have well-behaved cau…
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…
The study constructs pressure form on Margulis spacetimes and proves their infinitesimal rigidity.
problem Understanding the infinitesimal rigidity of Margulis spacetimes.
method Constructing pressure form and studying its properties on the moduli space of Margulis spacetimes.
result Margulis spacetimes are infinitesimally determined by their marked Margulis invariant spectra.
We describe in parallel the Lorentzian homogeneous spaces G=PSL(2,R) and g=psl(2,R), and review some recent results relating the geometry of their quotients by discrete groups.
We study proper, isometric actions of nonsolvable discrete groups Gamma on the 3-dimensional Minkowski space R^{2,1} as limits of actions on the 3-dimensional anti-de Sitter space AdS^3. To each such action is associated a deformation of a hyperbolic surface group Gamma_0 inside O(2,1). When Gamma_0 is convex cocompact…
The paper defines conditions for proper actions and relates them to Margulis spacetimes.
problem Understanding proper actions on specific geometric spaces.
method Analyzes Anosov representations and their infinitesimal versions.
result Interprets Margulis spacetimes as quotient manifolds of Hn,n−1. The paper proves a rigidity theorem for null geodesic travel times in asymptotically AdS spacetimes.
problem Determining if a spacetime is conformally AdS based on null geodesic travel times.
method Analyzing all null geodesics from a point to its antipodal point, considering various spacetime conditions.
result The spacetime is conformally AdS if and only if all null geodesics from a point refocus at its antipodal point.
Study shows Fredholmness of a Lorentzian Dirac operator on spacetimes.
problem Analyzing Fredholmness of a Lorentzian Dirac operator on spacetimes.
method Investigates Fredholmness of a (spatial) Γ-invariant Lorentzian Dirac operator under (anti) Atiyah-Patodi-Singer boundary conditions.
result Demonstrates Fredholmness of the operator in the von Neumann sense.
Future stability of a specific type of Kaluza-Klein spacetime is proven.
problem Stability of a particular class of Kaluza-Klein vacua.
method Einstein flow on a product manifold, Kaluza-Klein reduction, wave map type and Maxwell type equations, slice-adapted gauge.
result Future stability of the Milne universe within the class of spacetimes.
Researchers extend parametrization of Margulis spacetimes using strip deformations.
problem Parametrize Margulis spacetimes with decorated horoballs.
method Use strip deformations to parametrize complete finite-area hyperbolic surfaces with spikes decorated with horoballs.
result Generalized parametrization of Margulis spacetimes with photons.
Proves existence of solutions with concentrated energy in 2+1 spacetime.
problem Existence of solutions with concentrated energy in 2+1 spacetime.
method Direct treatment of 2+1 Einstein equations, novel scaling, Klainerman-Sobolev inequality.
result Uniform finite-time existence of solutions with positive incoming H1 energy. Study of caustics in Einstein-dust system, showing spacetime singularities and diverging curvature.
problem Understanding caustics and singularities in the Einstein-dust system.
method Established local existence result for spherically symmetric spacetimes containing caustics, constructed from solutions to a PDE problem.
result Obtained spherically symmetric spacetimes with diverging curvature and singular boundary.
Survey on extending Kleinian group theory to Lorentzian anti-de Sitter space.
problem Applying classical Kleinian group theory to Lorentzian anti-de Sitter space fails due to improper discontinuity and dependence of accumulation points.
method Introducing causality notions to extend limit sets and regularity domains to achronal subgroups.
result The theory of limit sets and regularity domains extends naturally to achronal subgroups in globally hyperbolic spacetimes.
We study the causality relation in the 3-dimensional anti-de Sitter space AdS and its conformal boundary Ein. To any closed achronal subset Λ in Ein_2 we associate the invisible domain E(Λ) from Λ in AdS. We show that if Γ is a torsion-free discrete group of isometries of AdS preserving Λ and is non-elem…
We classify and construct all the smooth Kaluza-Klein reductions to ten dimensions of the M2- and M5-brane configurations which preserve some of the supersymmetry. In this way we obtain a wealth of new supersymmetric IIA backgrounds describing composite configurations of D-branes, NS-branes and flux/nullbranes; bound s…
A new mathematical approach to general covariance using stacks and Lie algebras.
problem Understanding general covariance in curved spacetime field theories.
method Using stacks and groupoids to study the quotient of metrics modulo diffeomorphism, and analyzing the tangent complex and Lie algebra actions.
result Recovering a novel expression for the stress-energy tensor in scalar field theories.
Crooked planes were defined by Drumm to bound fundamental polyhedra in Minkowski space for Margulis spacetimes. They were extended by Frances to closed polyhedral surfaces in the conformal compactification of Minkowski space (Einstein space) which we call crooked surfaces. The conformal model of anti-de Sitter space is…
Study timelike bounce in charged null dust collapse, identifying key surfaces.
problem Understanding charged null dust collapse dynamics and bounce surfaces.
method Novel decoupling of equations, constructing spacetime models, solving free boundary problems.
result Timelike bounce surfaces identified in charged null dust collapse, including examples terminating in null points.
Unique invariant immersions found in Minkowski space.
problem Finding unique immersions of surfaces in Minkowski space.
method Functional introduced by Bonsante, Mondello & Schlenker, using Fuchsian groups and affine deformations.
result Unique affine deformation of a Fuchsian group exists, embedding surfaces with constant curvature.
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 shows how certain expanding spacetimes can collapse into flat or Kasner spacetimes.
problem Understanding the collapse of expanding vacuum spacetimes.
method Analysis of spacetimes with CMC foliations and scale invariant a priori bounds.
result Arbitrarily large future time intervals can be modelled by flat or Kasner 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.
Study directed completion of spacetimes, focusing on Schwarzschild spacetime.
problem Characterizing directed completions of spacetimes.
method Directed completion of Lorentzian pre-length spaces, focusing on Schwarzschild spacetime.
result Directed completion of Schwarzschild spacetime coincides with future causal completion.
Identifies all type D^k spacetimes in arbitrary dimensions.
problem Characterizing and distinguishing type D^k spacetimes.
method Analyzing curvature tensors and their invariants for degenerate Kundt metrics.
result Locally boost isotropic spacetimes are type D^k 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 paper examines the initial geometry of vacuum cosmological spacetimes and introduces new methods to characterize their behavior.
problem Characterizing the initial geometry of vacuum cosmological spacetimes.
method Analyzes Gowdy and non-Gowdy spacetimes with TN-actions, introduces a monotonic quantity for Kasner spacetimes, and uses curvature and volume bounds. result Evidence of AVTD behavior in Gowdy spacetimes and sufficient conditions for nonGowdy spacetimes.
Unique time function found for certain spacetimes with constant curvature.
problem Finding unique time functions with constant curvature in specific spacetimes.
method Proving existence of a unique foliation by hypersurfaces with constant scalar curvature.
result Existence of a unique time function with isochrones of constant scalar curvature.
Paper finds unique maximal hypersurfaces in open spacetimes.
problem Finding unique maximal hypersurfaces in open spacetimes.
method Natural geometric and physical assumptions applied to spatially open Robertson-Walker spacetimes with flat fiber.
result New uniqueness and non-existence results for complete maximal hypersurfaces.
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.
The paper classifies critical closed RW spacetimes using elliptic functions.
problem Classifying critical closed Robertson-Walker spacetimes.
method Study of critical RW spacetimes via volume-preserving variations and action functionals.
result Complete classification of critical RW spacetimes with explicit solutions.