Study flat spacetimes with BTZ singularities using BTZ-extension.
problem Understanding singularities in flat spacetimes.
method Use BTZ-extension to describe Moduli spaces and construct cauchy-surface.
result Construct convex polyhedral cauchy-surface in Cauchy-compact flat spacetimes with BTZ.
Extends flat spacetimes with BTZ singularities, preserving key properties.
problem Describing globally hyperbolic singular flat spacetimes.
method Lorentzian geometry, Teichmüller space, BTZ singularities.
result BTZ extensions preserve Cauchy-maximality and Cauchy-completeness.
Extending BTZ models to complete hyperbolic surfaces.
problem Extending BTZ models to complete hyperbolic surfaces.
method Proving a parametrization result for globally hyperbolic Cauchy-maximal and Cauchy-compact locally Minkowski manifolds with extreme BTZ.
result The tangent bundle of the Teichmüller space parametrizes globally hyperbolic Cauchy-maximal and Cauchy-compact locally Minkowski manifolds with extreme BTZ.
We revisit the non-rotating massive BTZ black hole within a pseudo-Riemannian symmetric space context. Using classical symmetric space techniques we find that every such space intrinsically carries a regular Poisson structure whose symplectic leaves are para-hermitian symmetric surfaces. We also obtain a global express…
Using ideas from an article of P. Bieliavsky, M. Rooman and Ph. Spindel on BTZ black holes, I construct a family of interesting examples of quasi-Poisson actions as defined by A. Alekseev and Y. Kosmann-Schwarzbach. As an application, I obtain a genuine Poisson structure on SL(2,R) which induces a Poisson structure o…
We study the relevant structure of so(2,n) which makes the BTZ black hole possible in the anti de Sitter space. We pay a particular attention of the reductive Lie algebra structures and Iwasawa decompositions and the way these structures evolves when one increases the dimension. The singularity is defined as the closed…
This paper is a sequel of "Solvable symmetric black hole in anti de Sitter spaces" [arXiv:math.DG/0510442]. In the latter, we described the BTZ black hole in every dimension by defining the singularity as the closed orbits of the Iwasawa subgroup of SO(2,n). In this article, we study the horizon of the black hole and w…
Using symmetric space techniques, we show that closed orbits of the Iwasawa subgroups of SO(2,l−1) naturally define singularities of a black hole causal structure in anti-de Sitter spaces in l≥3 dimensions. In particular, we recover for l=3 the non-rotating massive BTZ black hole. The method presented here i…
Study examines BTZ black hole using information geometry.
problem Understanding the BTZ black hole mechanism.
method Information geometry, Hessian potential, Legendre transformation.
result Exact BTZ metric and entanglement entropy derived.
This paper is the continuation of [8]. We essentially prove that the familly of strongly causal spacetimes defined in [8] associated to generic achronal subsets in Ein contains all the examples of BTZ multi black-holes. It provides new elements for the global description of these multi black-holes. We also prove that a…
In the first part we define a "BTZ" black hole in anti de Sitter space in any dimension by defining as "singular" the closed orbits of the Iwasawa component of SO(2,n). In the second part, a strict quantization of the black hole by action of group is performed and its Dirac operator is computed. We introduce, in the ap…
In the present paper the electrostatic of charges in non rotating BTZ black hole and wormhole space times is studied. In particular, the self force of a point charge in the geometry is characterized analitically. The differences between the self force in both cases is a theoretical experiment for distinguishing both ge…
The holographic description in the presence of gravitational Chern-Simons term is studied. The modified gravitational equations are integrated by using the Fefferman-Graham expansion and the holographic stress-energy tensor is identified. The stress-energy tensor has both conformal anomaly and gravitational or, if re-f…
In this paper we study several issues related to the generation of superpotential induced by background Ramond-Ramond fluxes in compactification of Type IIA string theory on Calabi-Yau four-folds. Identifying BPS solitons with D-branes wrapped over calibrated submanifolds in a Calabi-Yau space, we propose a general for…
A 'holographic formula' expressing the functional determinant of the scattering operator in an asymptotically locally anti-de Sitter(ALAdS) space has been proposed in terms of a relative functional determinant of the scalar Laplacian in the bulk. It stems from considerations in AdS/CFT correspondence of a quantum corre…
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…
Optimizes bounds for threefold singularity volumes.
problem Bounding local volumes of threefold singularities.
method Analyzes Gorenstein canonical non-hypersurface threefold singularities.
result Establishes optimal upper bound for local volumes.
Defines singular grid diagrams for various types of links.
problem Unified description of singular links and related objects.
method Definition of singular grid diagrams and classification of equivalence relations.
result Unified description of singular links and related objects.
Study describes singularities of height functions on specific singular surfaces.
problem Analyzing singularities of height functions on singular surfaces.
method Using geometric language and blowing-ups, investigate singularities of height functions and dual surfaces.
result Characterized singularities of height functions and dual surfaces on specific singular surfaces.
The paper extends affine connection results to singular warped and twisted products.
problem Generalizing affine connections to singular warped and twisted products.
method Study of singular multiply warped products and singular twisted products with semi-symmetric metric and non-metric connections, discussing Koszul forms and curvature.
result Theoretical results on curvature and Koszul forms for singular multiply warped and twisted products.
New singularity concept in GR: volume singularities.
problem Understanding spacetime singularities in General Relativity.
method Introducing a new type of singularity: volume singularities.
result Volume singularities are hidden by event horizons.
The study shows stability of neckpinch singularities in mean curvature flows.
problem Stability of neckpinch singularities in mean curvature flows.
method Analysis of mean curvature flow and perturbations.
result Stability of neckpinch singularities in mean curvature flows.
Study describes singularities of distance squared functions on singular surfaces.
problem Characterizing singularities of distance squared functions on singular surfaces.
method Using smooth map-germs Sk, Bk, Ck, and F4 singularities, the study describes singularities via blowing-ups. result Characterization of singularities of wave-fronts and caustics of singular surfaces.
Proves positive mass theorem for AF spin manifolds with conical singularities.
problem Proving the positive mass theorem for singular metrics on AF manifolds.
method Analyzes AF spin manifolds with isolated conical singularities, allowing topological singularities.
result Proves the positive mass theorem for AF spin manifolds with conical singularities.
The study examines singularities and geometric properties of surfaces derived from frontals with specific singular points.
problem Characterizing and understanding the singularities and geometric properties of surfaces formed by the singular loci of normal congruences of frontals with pure-frontal singular points.
method Characterizations of singularities in terms of geometric invariants of the initial frontal are provided for the normal ruled surface. Relations between certain singularities of focal surfaces and geometric properties of the frontal are also explored.
result Behavior of Gaussian curvature of focal surfaces of frontals with a 5/2-cuspidal edge is considered. Study singularities of Weinstein skeleta and arboreal singularities.
problem Understanding singularities in Weinstein skeleta and their relation to arboreal singularities.
method Deforming the skeleton via homotopies, Morse-Bott representative, generic perturbation, localization procedure.
result Singularities of Weinstein skeleta can be classified into arboreal singularities or tangency singularities.
Rectifies flat singular points of area-minimizing currents with singularity degree > 1.
problem Rectifying flat singular points of area-minimizing currents with singularity degree > 1.
method Subdividing singular points based on singularity degree and proving rectifiability of points with singularity degree > 1.
result The set of points with singularity degree > 1 is (m-2)-rectifiable.
The paper studies singularities of pedal curves of hyperbolic frontals.
problem Investigating singularities of pedal curves of spacelike frontals in hyperbolic 2-space.
method Analyzing singularities of pedal curves based on dual curve germs and pedal point locations.
result The singularities of pedal curves depend on the singularities of the first hyperbolic Legendrian curvature germ and the pedal point for non-singular dual curve germs. For singular dual curve germs, additional dependence on both Legendrian curvature germs is observed.
Paper generalizes a theorem for real analytic singularities.
problem No specific problem stated; focuses on generalization.
method Generalization of a theorem for complex singularities.
result Generalized Join theorem for real analytic singularities.
The paper extends deformation theory to Calabi-Yau varieties with isolated log canonical singularities.
problem Deformation theory of Calabi-Yau varieties with log canonical singularities.
method Study of higher Du Bois and rational singularities, focusing on 0-liminal singularities.
result Existence of first order smoothings for isolated 0-liminal hypersurface singularities.
Study on singular twisted links and virtual braids, extending knot theory concepts.
problem Extending knot theory concepts to singular twisted links and virtual braids.
method Definition and analysis of singular twisted virtual braids and their monoid structure.
result Presentation of monoid and reduced monoid for singular twisted virtual braids.
Maxfaces can have cuspidal edges near certain singularities.
problem Characterizing singularities on maxfaces.
method Analyzing singular Björling data and proving geometric properties.
result Near a maxface with a specific type of singularity, there exists another maxface with a cuspidal edge.
New invariant distinguishes singular knots and links.
problem Classifying singular knots and links.
method Using oriented singquandles and weight functions at crossings.
result Distinguishes singular granny knot from singular square knot.
Geodesics near singularities either hit or wind around, with winding number dependent on singularity type.
problem Understanding geodesic behavior near singularities in Riemannian manifolds.
method Analytical study of geodesics on Riemannian manifolds near singularities.
result The winding number of geodesics around a singularity depends on the singularity type and approaches infinity as the singularity becomes cuspidal.
This paper studies singular improper affine spheres from Lagrangian submanifolds, classifying stable singularities.
problem Understanding singularities of improper affine spheres from Lagrangian submanifolds.
method Analyzes canonical improper affine spheres and their on-shell singularities from Lagrangian submanifolds in arbitrary even dimensions.
result Classifies stable Lagrangian/Legendrian singularities on shell for improper affine spheres.
Defines algebraic structures from singular knot theory.
problem Distinguishing singular knots and links.
method Generalized Reidemeister moves and colorings.
result Set of colorings is an invariant of singular links.
Virtual singular braids are generalizations of singular braids and virtual braids. We define the virtual singular braid monoid via generators and relations, and prove Alexander- and Markov-type theorems for virtual singular links. We also show that the virtual singular braid monoid has another presentation with fewer g…
We study Legendrian singular links up to contact isotopy. Using a special property of the singular points, we define the singular connected sum of Legendrian singular links. This concept is a generalization of the connected sum and can be interpreted as a tangle replacement, which provides a way to classify Legendrian …
Study neck pinches in Lagrangian flows, proving stability and introducing new singularities.
problem Understanding neck pinches in Lagrangian flows.
method Introduced nondegenerate neck pinch and teardrop singularities, proving stability and answering questions.
result Nondegenerate neck pinches are stable and can be perturbed to nondegenerate singularities.
Criteria for Morin singularities in lower dimensions with applications to bifurcation.
problem Understanding Morin singularities in maps into lower dimensions.
method Providing criteria for Morin singularities and studying bifurcations of Lefschetz singularities.
result Criteria for Morin singularities in maps into lower dimensions.
Generates moves for oriented singular links using algebraic structures.
problem Understanding and distinguishing oriented singular links.
method Introduced algebraic structures to study oriented singular knots and links.
result Colorings of singular knots by new algebraic structures are invariants and distinguish some links.
Classifies neighborhoods around specific leaf structures.
problem Classifying singular foliations with given leaf and transverse singular foliation.
method Analyzes the structure of singular foliations and their leaves.
result Developed a method to classify neighborhoods around specific leaf structures.
We study the local symplectic algebra of curves. We use the method of algebraic restrictions to classify symplectic T7 singularities. We define discrete symplectic invariants - the Lagrangian tangency orders. We use these invariants to distinguish symplectic singularities of classical A−D−E singularities of planar…
Study calculates Euler obstruction for determinantal varieties with ICIS singular set.
problem Calculating Euler obstruction for determinantal varieties with ICIS singular set.
method Obtained formulas to calculate Euler obstruction for determinantal varieties with ICIS singular set.
result Formulas to calculate the Euler obstruction for determinantal varieties with ICIS singular set.
The article investigates conditions for isomorphism of singular tangent bundles.
problem Conditions for isomorphism of singular tangent bundles.
method Logarithmic and b-tangent bundles approach to resolve singularities. result Established a Poincaré-Hopf theorem for bm-tangent bundles. Singular fibrations over surfaces generalize Lefschetz fibrations and have new construction methods.
problem Understanding and constructing singular fibrations over surfaces.
method Explains how to construct examples of singular fibrations with a single singularity and outlines previous results.
result Closed orientable 4-manifolds with large first Betti number and vanishing second Betti number do not admit singular fibrations.
This thesis studies moduli spaces of singular connections on 3-manifolds and manifolds with cylindrical ends. A Chern-Simons functional is defined for singular connections on 3-manifolds which are singular along a knot. The critical points of that Chern-Simons functional are flat singular connections. The Hodge-de Rham…
Defines generic singularities in planar flat 3-webs and classifies them.
problem Classifying singularities in planar flat 3-webs.
method Proposes a definition of genericity and classifies singularities.
result Classifies generic singularities of planar flat 3-webs.