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 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. For 2+1 spacetime dimensions, we derive sufficient conditions for the twisting function in a twisted product spacetime, such that there is a global foliation by spacelike CMC surfaces.
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.
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…
Study of spacelike hypersurfaces in twisted product spacetimes with specific conditions.
problem Characterizing and understanding spacelike hypersurfaces in twisted product spacetimes.
method Analysis of conditions ensuring global hyperbolicity, use of conformal geometry results.
result Non-existence results for constant mean curvature hypersurfaces under certain conditions.
Spinors prove rigidity for polyhedral spacetime data.
problem Rigidity of polyhedral spacetime data sets.
method Extending rigidity analysis from spacetime positive mass theorem.
result Dihedral rigidity connects mass theorem, trapped surfaces.
We begin by presenting a symmetric version of the circle equivariant T-duality result in a joint work of the second author with Siye Wu, thereby generalising the results there. We then initiate the study of twisted equivariant Courant algebroids and equivariant generalised geometry and apply it to our context. As befor…
In this paper, we compute the index form of the multiply twisted products. We study the Killing vector fields on the multiply twisted product manifolds and determine the Killing vector fields in some cases. We compute the curvature of the multiply twisted products with a semi-symmetric metric connection and show that t…
Formula for index in Lorentzian spacetimes.
problem Developing an index formula for spacetimes with boundary.
method Reduction from equivariant to non-equivariant, Lorentzian spectral flow.
result Equivalence of equivariant index and spectral flow in Lorentzian spacetimes.
Topological twists for 4d N=2 theories depend on spacetime type, gerbe connections, and generalized spin-c structures.
problem Defining topologically twisted partition functions for 4d N=2 theories.
method Topological twisting for general 4d N=2 theories, introducing generalized spin-c structures.
result Topological partition functions depend on spacetime type, gerbe connections, and generalized spin-c structures.
In the present paper we provide new examples of marginally trapped surfaces and tubes in FLRW spacetimes by using a basic relation between these objects and CMC surfaces in 3-manifolds. We also provide a new method to construct marginally trapped surfaces in closed FLRW spacetimes, which is based on the classical Hopf …
This study analyzes a non-orientable spacetime model in 1+1D quantum gravity.
problem Analyzing a non-orientable spacetime model in 1+1D quantum gravity.
method Formulated a Jackiw-Teitelboim gravity toy model on the Möbius band, computed Stiefel-Whitney classes, and analyzed the Dirac operator.
result Half-integer momentum quantization, spectral symmetry, vanishing mod-2 index, and η_D(0) = 0 follow.
New self-similarity for Einstein vacuum equations identified.
problem Understanding spacetime behavior near singularities.
method Systematic geometric characterization and formal expansions.
result Twisted self-similar solutions cover all asymptotic behaviors.
Vortex solutions on flat surfaces map to harmonic spinors on Nappi-Witten space.
problem Constructing Abelian magnetic zero-modes on flat spacetime.
method Establishing a correspondence between vortex equations and harmonic spinors on the Nappi-Witten space.
result Explicit solutions of a twisted Dirac equation induce harmonic spinors on Minkowski space.
We present an explicit formula for the topology and H-flux of the T-dual of a general type II compactification, significantly generalizing earlier results. Our results apply to T-dualities with respect to any circle action on spacetime. As before, T-duality exchanges type IIA and type IIB string theories. A new consequ…
Paper establishes loop space T-duality formulae and refines earlier work.
problem Establishing T-duality on loop spaces with background flux.
method Developed loop Hori map and twisted Bismut-Chern character.
result Loop Hori map induces quasi-isomorphism on loop spaces.
We show that there is a correspondence between totally umbilic null hypersurfaces in generalized Robertson-Walker spaces and twisted decompositions of the fibre. This allows us to prove that nullcones are the unique totally umbilic null hypersurfaces in the closed Friedmann Cosmological model. We also apply this kind o…
Departing from the observation that the Penrose limit of AdS_3 x S^3 is a group contraction in the sense of Inonu and Wigner, we explore the relation between the symmetric D-branes of AdS_3 x S^3 and those of its Penrose limit, a six-dimensional symmetric plane wave analogous to the four-dimensional Nappi--Witten space…
In superstring theory spin structures are present on both the 2-dimensional worldsheet and 10-dimensional spacetime. We present a new proposal for the B-field in superstring theory and demonstrate its interaction with worldsheet spin structures. Our formulation generalizes to orientifolds, where various twistings appea…
Study properties of hypersurfaces in spacetimes with conformal transformations.
problem Properties of embedded hypersurfaces in spacetimes with a preferred spatial direction.
method Analysis of hypersurfaces with conformal transformations, scalar curvature conditions, and Riemannian manifold properties.
result Hypersurfaces are either Einstein or have vanishing twist, and under certain conditions, they are isomorphic to the 3-sphere.
Given a semi-Riemannian 4-manifold (M,g) with two distinguished vector fields satisfying properties determined by their shear, twist and various Lie bracket relations, a family of Kähler metrics gK is constructed, defined on an open set in M, which coincides with M in many typical examples. Under certain con…
The study identifies obstructions to global visibility of singularities in spacetimes.
problem Identifying conditions that prevent singularities from being globally visible in asymptotically flat spacetimes.
method Developed two generator-wise criteria using the Raychaudhuri equation and Sturm-type ODEs.
result Existence of focal points implies non-global visibility of singularities.
We consider the topological and geometric structures associated with cohomological and homological objects in M-theory. For the latter, we have M2-branes and M5-branes, the analysis of which requires the underlying spacetime to admit a String structure and a Fivebrane structure, respectively. For the former, we study h…
A geometric string solution has background fields in overlapping coordinate patches related by diffeomorphisms and gauge transformations, while for a non-geometric background this is generalised to allow transition functions involving duality transformations. Non-geometric string backgrounds arise from T-duals and mirr…
We give a concise summary of the para-Hermitian geometry that describes a doubled target space fit for a covariant description of T-duality in string theory. This provides a generalized differentiable structure on the doubled space and leads to a kinematical setup which allows for the recovery of the physical spacetime…
Modernizes higher-dimensional supergravity, linking it to flux quantization.
problem Constructing infrared completions of higher-dimensional supergravity.
method Using differential nonabelian cohomology and super-torsion constraints.
result Equivalence of solutions in different dimensions and flux quantization.
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 paper derives inequalities and formulas for generalized Ricci flow.
problem Understanding and characterizing generalized Ricci flow.
method Using Bochner formula and adapted Malliavin gradient, the paper derives inequalities and characterizes generalized Ricci flow.
result Characterizations of generalized Ricci flow via inequalities for the associated Malliavin gradient.
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. Kaluza-Klein Theory states that a metric on the total space of a principal bundle P→M, if it is invariant under the principal action of P, naturally reduces to a metric together with a gauge field on the base manifold M. We propose a generalization of this Kaluza-Klein principle to higher principal bun…
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.
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.
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…
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.