Defines a geometric dimension for Lorentzian spaces, distinguishing spacelike and null subspaces.
problem No specific problem stated; focuses on defining a new geometric dimension.
method Introduces a one-parameter family of volume measures and a doubling condition for causal diamonds.
result Defines a geometric dimension for synthetic spacetimes, distinguishing between spacelike and null subspaces.
New approach to finite gauge transformations in doubled spacetime.
problem Complexity of finite gauge transformations in double field theory.
method Intuitive approach using untwisted vector fields and maximal null subspace.
result Finite transformation law automatically satisfies composition law and avoids the Papadopoulos problem.
The paper studies optical properties in de Sitter spacetimes.
problem Stability of expanding regions in Schwarzschild de Sitter spacetimes.
method Construction of global solutions to the eikonal equation and detailed estimates of structure coefficients.
result Globally well-behaved double null foliations can be constructed from infinity.
The paper studies hyperbolic equations in a spacetime foliation, proving existence and uniqueness.
problem Existence and uniqueness of solutions for first-order linear hyperbolic systems in a double null foliation.
method Proves global existence and uniqueness for first-order linear hyperbolic systems with initial data on a past null hypersurface.
result Derives a novel algebraic constraint for tensorfields satisfying the linearized Bianchi equations.
Paper defines and proves geometric uniqueness of Einstein field equations.
problem Einstein field equations characteristic Cauchy problem
method Covariant definition of double null data, proving geometric uniqueness
result Double null data fully covariant and geometrically unique
We construct a C-space associated with every closed 3-form on a spacetime M and show that it depends on the class of the form in H3(M,Z). We also demonstrate that C-spaces have a relation to generalized geometry and to gerbes. C-spaces are constructed after introducing additional coordinates at the open sets and …
Stability of a special spacetime solution is proven under certain symmetries.
problem Understanding the long-time behavior of cosmological solutions with symmetries.
method Proves stability of double-cusp spacetime solution under small T2-symmetry-preserving perturbations.
result Double-cusp solution is stable under small T2-symmetry-preserving perturbations.
The study examines extensions of a projective plane minus two discs in flat affine Lorentzian 3-manifolds.
problem Classifying proper actions of affine Coxeter extensions on Minkowski space.
method Investigates double extensions of fundamental groups and their actions on Minkowski space.
result Identifies proper actions of the double extension that do not admit crooked fundamental domains.
Global Double Field Theory is a higher-dimensional generalization of Kaluza-Klein theory.
problem Formulating a global theory for higher-dimensional gauge fields.
method Generalizing Kaluza-Klein theory to higher principal bundles and higher gauge fields.
result Higher Kaluza-Klein geometry provides a global formulation for Double Field Theory.
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.
Modeling wildfire spread using Gielis superformula and Finsler spacetime.
problem Accurately modeling the short-time spread of wildfires.
method Using Gielis superformula and Finsler spacetime to determine firefronts.
result A concise and efficient expression of geodesic equations.
This work applies Double Field Theory to four-dimensional manifolds, revealing connections to integrability and twistor theory.
problem Understanding dualities in string theory and their geometrical structures.
method Generalized and para-Hermitian geometry applied to four-dimensional manifolds.
result Close relationship between para-Hermitian structures in Double Field Theory and algebraically special solutions to Einstein equations.
The paper defines marginal tubes and proves their null nature.
problem Understanding the geometry of spacelike surfaces in spacetimes.
method Introducing marginal tubes and studying spacelike surfaces with double null coordinates.
result If every spacelike section of a marginal tube is a marginal surface, then the marginal tube is null.
The study examines algebraic structures of specific tensor forms in four-dimensional spacetimes.
problem Investigating algebraic features of certain tensor forms in spacetimes.
method General treatment followed by specialization to four-dimensional spacetimes, focusing on invariant subspaces and generalizing relations.
result Generalized relations such as the Ruse-Lanczos identity, Bel-Matte decomposition, and Lovelock-like quadratic identities.
Study of marginally trapped surfaces in a perturbed Schwarzschild spacetime.
problem Understanding marginally trapped surfaces in perturbed Schwarzschild spacetime.
method Developed a method to study spacelike surfaces in a double null coordinate system.
result For every incoming null hypersurface nearly spherically symmetric, there exists a unique embedded marginally trapped surface.
The paper proves the Null Penrose Inequality for Schwarzschild spacetimes.
problem Proving the Null Penrose Inequality for Schwarzschild spacetimes.
method Introducing quasi-round MOTSs and showing their stability and existence for specific horizons.
result Identifies sufficient conditions for the Null Penrose Inequality in Schwarzschild spacetimes.
Researchers extend microlocal analysis across event horizons of rotating black holes.
problem Incomplete microlocal theory of fields across black hole event horizons.
method Extended microlocal theory for extremal rotating black holes, showing null covectors form an involutive double characteristic manifold.
result Mathematical basis for asymptotic oscillatory solutions near event horizons.
We solve Bartnik's stationary extension problem near Schwarzschild spheres.
problem Existence and uniqueness of asymptotically flat stationary vacuum spacetimes.
method Developed a double geodesic gauge, reducing equations to elliptic and transport-type problems.
result Local well-posedness for Bartnik stationary metric extension problem near Schwarzschild spheres.
The paper examines the stability of two spherical self-similar solutions in Minkowski spacetime.
problem Stability of timelike extremal hypersurfaces in Minkowski spacetime.
method Analysis of linear and nonlinear stability, construction of Newton's polygon.
result Explicit lightlike self-similar solutions are nonlinearly stable inside a subset of the backward lightcone.
A characterization of the Kerr-NUT-(A)de Sitter metric among four dimensional Λ-vacuum spacetimes admitting a Killing vector is obtained in terms of the proportionality of the self-dual Weyl tensor and a natural self-dual double two-form constructed from the Killing vector. This result recovers and extends a previous c…
The notion of wind Finslerian structure is developed; this is a generalization of Finsler metrics where the indicatrices at the tangent spaces may not contain the zero vector. In the particular case that these indicatrices are ellipsoids, called here wind Riemannian structures, they admit a double interpretation which …
Summary of para-Hermitian geometry for T-duality in string theory.
problem Describing T-duality in string theory with a covariant approach.
method Introducing para-Hermitian geometry and Born geometry to enhance the kinematical setup.
result A generalized differentiable structure on the doubled space allows for the recovery of physical spacetime.
Paper introduces a new convergence for Lorentzian spaces using causal diamonds.
problem No specific problem stated; focuses on a new geometric convergence.
method Uses causal diamonds to define a new convergence for Lorentzian spaces.
result Proves a pre-compactness theorem for Lorentzian spaces.
New spaces at infinity identified for Minkowski spacetime.
problem Characterizing asymptotic infinities of Minkowski spacetime.
method Embedding and describing homogeneous spaces of the Poincaré group.
result Determined new structures on asymptotic infinities.
Unified super-symmetry and higher fluxes using super-Lie-infinity algebras.
problem Unified extended super-symmetry and higher flux densities.
method Using super-Lie-infinity algebras and their extensions and cyclifications.
result Derivation of topological T-duality laws from super-Lie-infinity structure.
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.
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…
Proves stability of Schwarzschild black holes without symmetry assumptions.
problem Stability of Schwarzschild black holes under general conditions.
method Teleologically normalised double null gauges, analysis of linear stability, and control of non-linearities.
result Proves non-linear asymptotic stability of Schwarzschild family as solutions to Einstein vacuum equations.
Introduces D-branes in para-Hermitian geometries using T-duality.
problem Defines D-branes in a new geometric framework.
method Uses para-Hermitian geometry and metric algebroids to define D-branes as conformal boundary conditions for open strings.
result Reveals D-branes as para-complex versions of topological A/B-branes.
The hidden M-algebra is integrated into a super-Lie group, allowing for compactification of extra dimensions.
problem Integrating the hidden M-algebra into a super-Lie group to model super-exceptional spacetimes.
method Left-invariant extension of the decomposed M-theory 3-form, providing a computer-checked re-derivation and streamlined conception of super-Lie groups.
result Lattice subgroups of the hidden M-group allow toroidal compactification of hidden dimensions, akin to topological T-duality.
Solves characteristic problem in general relativity for null data.
problem Characteristic Cauchy problem in Einstein vacuum field equations.
method Abstract data formalism and tangential components of the ambient Ricci tensor.
result Formulates and solves the characteristic problem completely abstractly.
New proof of Schwarzschild stability using geometric gauge.
problem Linear stability of Schwarzschild spacetime under gravitational perturbations.
method Employing a new geometric gauge and exploiting the structure of transport equations.
result Established both orbital and asymptotic stability for linearised quantities.
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.
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 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.
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.