Null geodesics spaces can be embedded into globally hyperbolic spacetimes.
problem Obstructing conformal embeddings of causally simple spacetimes.
method Analyzing null geodesics and conformal embeddings.
result Causally simple spacetimes can be non-conformally embeddable into globally hyperbolic ones.
Study shows contact structure on null geodesic space for specific spacetimes.
problem Understanding contact structures on null geodesic spaces of spacetimes.
method Contactomorphism and embedding techniques in spherical cotangent bundles.
result Space of null geodesics contactomorphic to canonical structure in spherical cotangent bundle.
We formulate the generalization of the Legendrian Low conjecture of Natario and Tod (proved by Nemirovski and myself before) to the case of causally simple spacetimes. We prove a weakened version of the corresponding statement. In all known examples, a causally simple spacetime (X,g) can be conformally embedded as a…
The paper proves a conjecture about spacetimes and singularities.
problem Understanding naked singularities and causally simple spacetimes.
method Analyzes null geodesics and spacetime properties to prove conjectures.
result Proves a conjecture about spacetimes and singularities, including implications for two-dimensional spacetimes.
Continuous Lorentzian metrics yield infinitesimal Minkowskian spacetimes.
problem Understanding spacetime properties from continuous Lorentzian metrics.
method Proving infinitesimal Minkowskianity for causally simple metric measure spacetimes.
result Continuous Lorentzian metrics result in spacetimes that are infinitesimally Minkowskian.
A simple characterization of the causal automorphisms of 1+1 Minkowski spacetime is given.
New findings on lightconvex boundaries in Finslerian spacetimes.
problem Understanding causal structures in Finslerian spacetimes.
method General results for indefinite Finslerian manifolds with boundary, and equivalence among boundary lightconvexity, causally simple interior, and Hausdorff space of cone geodesics.
result Equivalence among boundary lightconvexity, causally simple interior, and Hausdorff space of cone geodesics in globally hyperbolic spacetimes.
Khovanov homology detects causality in spacetimes.
problem Detecting causality in spacetimes.
method Khovanov homology applied to (2+1)-dimensional spacetimes. result Khovanov homology detects causality in specific spacetimes.
Causal spacetimes with Ricci tensor have unique transformations.
problem Understanding transformations in viable causal spacetimes.
method Analyzing Ricci tensor and causal diffeomorphisms.
result Causal diffeomorphisms preserving Ricci tensor are homotheties.
Detect spacetime curvature with event causality measurements.
problem Detecting spacetime curvature without rulers and clocks.
method Prove spacetime non-flatness through causal relations.
result Sixteen measurements verify non-flatness of non-conformally flat spacetimes.
The causal structure of a strongly causal spacetime is particularly well endowed. Not only does it determine the conformal spacetime geometry when the spacetime dimension n >2, as shown by Malament and Hawking-King-McCarthy (MHKM), but also the manifold dimension. The MHKM result, however, applies more generally to spa…
Study causal structure of warped spacetimes using novel pre-length spaces.
problem Understanding the causal structure of warped spacetimes.
method Novel notion of Lorentzian pre-length spaces and proof of causal completion as globally hyperbolic pre-length space.
result Causal completion of GRW spacetime is a globally hyperbolic pre-length space under Hausdorff chronological topology.
Researchers examine various causal structures for spacetimes with continuous metrics.
problem Comparing causal structures for spacetimes with continuous but not necessarily smooth metrics.
method Examined three key properties: push-up lemma, openness of chronological futures, and existence of limit causal curves.
result Spacetimes with continuous metrics do not always satisfy all three key properties.
Counterexample disproves Borde-Sorkin conjecture on causal continuity of Morse spacetimes.
problem Disproving the Borde-Sorkin conjecture on causal continuity of Morse spacetimes.
method Provided a counterexample with low regularity causal structure and causal bubbling.
result Borde-Sorkin conjecture does not hold for Morse spacetimes with large anisotropy.
We obtain some results in both Lorentz and Finsler geometries, by using a correspondence between the conformal structure (Causality) of standard stationary spacetimes on M=R×S and Randers metrics on S. In particular, for stationary spacetimes, we give a simple characterization of when they are causally conti…
Causal classification of three Misner-type spacetimes.
problem Causal structure and isocausality of three spacetimes.
method Formal proof of pairwise isocausality on covers and compactified spacetimes.
result Explicit causal bijections and deck-equivariance criterion for isocausality.
Enhanced symplectic quandle colorings detect causal structure in spacetime diagrams.
problem Detecting causal structure in spacetime diagrams using polynomial invariants.
method Comparing symplectic quandle colorings of different diagrams representing spacetime connections.
result Enhanced symplectic quandle colorings consistently distinguish between causally unrelated and related spacetime configurations.
Example of spacetime with causal bubbling, splitting into timelike and spacelike parts.
problem Understanding causal bubbling in spacetimes.
method Example of a globally hyperbolic spacetime with a continuous metric, splitting orthogonally into timelike and spacelike parts.
result The synthetic timelike curvature-dimension (TCD) condition does not prevent causal bubbling.
This paper gives a new proof that maximal, globally hyperbolic, flat spacetimes of dimension n≥3 with compact Cauchy hypersurfaces are globally foliated by Cauchy hypersurfaces of constant mean curvature, and that such spacetimes admit a globally defined constant mean curvature time function precisely when they a…
In this work we will focus on the causal character of Carter Spacetime (see B. Carter, Causal structure in space-time, Gen. Rel. Grav. 1 4 337-406, 1971). The importance of this spacetime is the following: for the causally best well behaved spacetimes (the globally hyperbolic ones), there are several characterizations …
Study baryogenesis in conformally flat spacetimes using causal fermion systems.
problem Understanding baryogenesis in specific spacetimes.
method Analysis of baryogenesis mechanism in conformally flat spacetimes with explicit formula derivation.
result Explicit formula for baryogenesis rate in these spacetimes.
No closed timelike geodesics in Kerr spacetimes, proving absence of closed causal geodesics.
problem Proving the nonexistence of closed timelike geodesics in Kerr spacetimes.
method Analyzing the Kerr-star spacetime, excluding closed null geodesics and proving the nonexistence of closed timelike geodesics.
result No closed timelike geodesics in Kerr spacetimes.
This paper completes globally hyperbolic conformally flat spacetimes, proving they are topological manifolds.
problem Understanding the structure of spacetimes with specific properties.
method Analyzing globally hyperbolic conformally flat spacetimes, proving their causal completions are topological manifolds.
result Causal completions of globally hyperbolic conformally flat spacetimes are topological manifolds homeomorphic to S x [0, 1].
Proves a positive mass theorem for static causal fermion systems.
problem Defining mass for complex spacetimes without regularity assumptions.
method Surface layer integrals comparing asymptotically flat and vacuum spacetimes.
result Proves a positive mass theorem for static causal fermion systems.
The paper studies convergence of cosmological spacetimes using null distance.
problem Convergence of cosmological spacetimes with compact slices.
method Using null distance and Gromov-Hausdorff convergence, the paper establishes convergence results for spacetimes with mild extension properties.
result Uniform convergence of null distances and Gromov-Hausdorff convergence for monotone sequences of spacetimes.
Empirical evidence suggests link polynomials can detect causality in spacetimes.
problem Detect causality in (2+1)-dimensional globally hyperbolic spacetimes. method Introduced a new invariant of certain tangles related to the Conway polynomial.
result The Conway polynomial does not detect causality in certain spacetime scenarios.
In a recent paper, Eichmair, Galloway and Pollack have proved a Gannon-Lee-type singularity theorem based on the existence of marginally outer trapped surfaces (MOTS) on noncompact initial data sets for globally hyperbolic spacetimes. This result requires that the MOTS be generic in a suitable sense. In the same spirit…
Quandle coloring detects causality in spacetime links.
problem Detecting causality in spacetime links using quandle colorings.
method Conjugation quandle of dihedral group D5 combined with Alexander-Conway polynomial.
result The conjugation quandle over D5 distinguishes causally related and unrelated events.
The paper establishes criteria for spacetime inextendibility using asymptotic volume-distance-ratio analysis.
problem Determining inextendibility of spacetimes near singularities.
method Asymptotic analysis of volume-distance-ratio (VDR) to prove inextendibility criteria.
result Failure of VDR convergence to the Minkowski value implies inextendibility of spacetime.
The group of conformal diffeomorphisms and the group of causal automorphisms on two-dimensional globally hyperbolic spacetimes are clarified. It is shown that if spacetimes have non-compact Cauchy surfaces, then the groups are subgroups of that of two-dimensional Minkowski spacetime, and if spacetimes have compact Cauc…
Study examines two topologies on future causal completion of spacetimes.
problem Characterizing differences between two topologies on future causal completion.
method Systematic examination of the stronger topology τ+ on Geroch-Kronheimer-Penrose future completion IP(X) of spacetimes X. result Complete characterization of the difference in convergence between τ+ and the weaker topology. Minimal TIP and TIF found in compact spacetimes, impacting spacetime splitting.
problem Understanding the global structure of spacetimes with compact Cauchy surfaces.
method Analysis of Terminal Indecomposable Past (TIP) and Future (TIF) sets in spacetimes with compact Cauchy surfaces.
result In a spacetime with compact Cauchy surfaces, there is always at least one minimal TIP and one minimal TIF.
The folk questions in Lorentzian Geometry, which concerns the smoothness of time functions and slicings by Cauchy hypersurfaces, are solved by giving simple proofs of: (a) any globally hyperbolic spacetime (M,g) admits a smooth time function τ whose levels are spacelike Cauchy hyperfurfaces and, thus, also a smooth…
Study of isometries in spacetimes without observer horizons.
problem Understanding the symmetries of spacetimes without specific boundaries.
method Analysis of isometry groups in causal spacetimes without observer horizons.
result The group of time orientation-preserving isometries acts properly on the spacetime.
Note: Causality can be encoded without strict time function choice.
problem Global encoding of causality under natural conditions.
method Observation of weakening causality assumptions in existing results.
result Causality can be encoded without strict time function choice.
Kerr spacetimes without closed null geodesics for non-zero rotation.
problem Analyzing closed geodesics in Kerr spacetimes.
method Analytic extension and geodesic analysis.
result Kerr spacetimes do not admit closed null geodesics for any non-zero rotation parameter.
Globally hyperbolic spacetimes admitting infinitely many causal (and timelike) homotopy classes of curves joining two prescribed points, are exhibited and discussed.
New topology defined from spacetime paths, reconstructing spacetime structure.
problem Reconstructing spacetime structure from path homotopy classes.
method Defining a topology on spacetime based on timelike and causal homotopy classes.
result The topology on spacetime is reconstructed from the space of homotopy classes.
We develop a new approach to the existence of time functions on Lorentzian manifolds, based on Conley's work regarding Lyapunov functions for dynamical systems. We recover Hawking's result that a stably causal admits a time function through a more general result giving the existence of a continuous function that is non…
Several uniqueness results on compact maximal hypersurfaces in a wide class of sta- bly causal spacetimes are given. They are obtained from the study of a distinguished function on the maximal hypersurface, under suitable natural first order conditions of the spacetime. As a consequence several applications to Geometri…
An important question that discrete approaches to quantum gravity must address is how continuum features of spacetime can be recovered from the discrete substructure. Here, we examine this question within the causal set approach to quantum gravity, where the substructure replacing the spacetime continuum is a locally f…
Symplectic quandles can detect causality in spacetimes, improving on existing methods.
problem Detecting causality in (2+1)-dimensional spacetimes using existing methods.
method Combining Alexander-Conway polynomial with symplectic quandles.
result Symplectic quandles can distinguish between different types of links, suggesting their ability to detect causality.
Recently ({\em Class. Quant. Grav.} {\bf 20} 625-664) the concept of {\em causal mapping} between spacetimes --essentially equivalent in this context to the {\em chronological map} one in abstract chronological spaces--, and the related notion of {\em causal structure}, have been introduced as new tools to study causal…
New relation between curvature bounds and spacetime inextendibility.
problem Inextendibility of spacetimes under low regularity conditions.
method Synthetic curvature and causal character analysis.
result Low-regularity spacetimes with unbounded curvature.
Reconstruct spacetime from order and number of points.
problem Reconstruct spacetime from chronological relations and i.i.d. samples.
method Relaxing hypotheses of Gromov reconstruction theorem, using random adjacency matrices and chronological relations.
result Spacetime can be recovered by only knowing 'order' and 'number' of its points.
Generic singularities found in spacetimes with weakly trapped submanifolds.
problem Existence of singularities in spacetimes with weakly trapped submanifolds.
method Using Whitney topologies and singularity theorems, the study shows genericity of singularities in spacetimes with weakly trapped submanifolds.
result Generic singularities are found in spacetimes with weakly trapped submanifolds.
New results on non-existence and rigidity of spacelike submanifolds in spacetimes.
problem Non-existence and rigidity of spacelike submanifolds with causal mean curvature vector field.
method General results for various spacetimes including globally hyperbolic, stationary, and pp-wave spacetimes.
result Significant consequences in Geometrical Analysis, solving new Calabi-Bernstein and Dirichlet problems.
New relation between curvature bounds and spacetime inextendibility.
problem Inextendibility of spacetimes under low regularity conditions.
method Synthetic curvature and causal character maximizers.
result Low-regularity inextendibility linked to unbounded curvature.