arXiv research

We consider four-dimensional vacuum spacetimes which admit a nonvanishing spacelike Killing field. The quotient with respect to the Killing action is a three-dimensional quotient spacetime $(M,g)$. We establish several results regarding maximal hypersurfaces (spacelike hypersurfaces of zero mean curvature) in such quot…

The paper classifies coverings and non-Hausdorff extensions of Misner spacetime.

Affine deformations of convex cones yield special spacetime structures.

This study explores Kaluza-Klein reductions of new maximally supersymmetric backgrounds.

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 $\geq 2$. 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…

We describe in parallel the Lorentzian homogeneous spaces $G=\mathrm{PSL}(2,\mathbb{R})$ and $\mathfrak{g}=\mathfrak{psl}(2,\mathbb{R})$, 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…

In this article we construct the pressure form on the moduli space of higher dimensional Margulis spacetimes without cusps and study its properties. We show that the Margulis spacetimes are infinitesimally determined by their marked Margulis invariant spectrums. We use it to show that the restrictions of the pressure f…

The paper proves a rigidity theorem for null geodesic travel times in asymptotically AdS spacetimes.

Study shows Fredholmness of a Lorentzian Dirac operator on spacetimes.

Researchers extend parametrization of Margulis spacetimes using strip deformations.

Proves existence of solutions with concentrated energy in 2+1 spacetime.

Study of caustics in Einstein-dust system, showing spacetime singularities and diverging curvature.

Classical Kleinian groups are discrete subgroups of isometries of H n. The well-known theory of Kleinian groups starts with the definition of their associated limit set in the boundary of H n , and includes the geometric properties of the quotient hyperbolic space. This approach, naively applied, fails in the Lorentzia…

We consider the Einstein flow on a product manifold with one factor being a compact quotient of 3-dimensional hyperbolic space without boundary and the other factor being a flat torus of fixed arbitrary dimension. We consider initial data symmetric with respect to the toroidal directions. We obtain effective Einsteinia…

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…

In this article, we provide a necessary and sufficient criterion for proper actions on $\mathbb{H}^{n,n-1}$ in terms of certain special Anosov representations in $\mathsf{SO}(n,n)$. Moreover, we show that affine Anosov representations of any word hyperbolic group in $\mathsf{SO}(n,n-1)\ltimes\mathbb{R}^{2n-1}$ are infi…

A new mathematical approach to general covariance using stacks and Lie algebras.

Let $S$ be a compact, orientable surface of hyperbolic type. Let $(k_+,k_-)$ be a pair of negative numbers and let $(g_+, g_-)$ be a pair of marked metrics over $S$ of constant curvature equal to $k_+$ and $k_-$ respectively. Using a functional introduced by Bonsante, Mondello \& Schlenker, we show that there exists a …

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.

The paper finds conditions for pseudosymmetric spacetimes to be perfect fluids.

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.

The paper introduces and analyzes pseudo generalized Ricci-recurrent spacetimes in modified gravity.

The study characterizes spacetimes with quasi-constant sectional curvature and explores their properties in $\mathcal{F}(\mathcal{R})$-gravity.

The article introduces pseudo generalized Ricci-recurrent spacetimes and their applications in modified gravity.

The paper studies the past inextendibility of FLRW spacetimes using the VDR asymptote.

Study explores geometric properties of Vaidya-Bonner-de Sitter spacetime.

The study characterizes GRW spacetimes with gradient solitons and phantom era.

Characterizes Lorentzian manifolds embeddable in Minkowski spacetime.

New proof shows FLRW spacetimes can't be extended smoothly in certain axisymmetric cases.

Study of quasilocal mass using isometric embedding in various spacetimes.

Characterizes pseudo B-symmetric spacetimes and their implications in f(R) gravity.

Characterizes a specific type of spacetime using vector fields.

Study maximal hypersurfaces in open spacetimes using a maximum principle.

The study explores properties of a specific type of spacetime.

New findings show cosmological constant as initial condition for non-isotropic spacetimes.

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 ${\bf D}$ relative to some common null frame. Such spacetimes are known as type ${\b…

Study finds unique and non-existent constant mean curvature hypersurfaces in specific spacetimes.

New Galilean spacetimes found as pp-wave reductions.

Study revisits Bondi mass and discusses memory effect in polyhomogeneous spacetimes.

Study baryogenesis in conformally flat spacetimes using causal fermion systems.

In 2+1 dimensions, all complete spacetimes are cylindrical.

The study examines perfect fluid spacetimes and their properties.