A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Causal spacetimes with Ricci tensor have unique transformations.
Detect spacetime curvature with event causality measurements.
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.
Researchers examine various causal structures for spacetimes with continuous metrics.
Counterexample disproves Borde-Sorkin conjecture on causal continuity of Morse spacetimes.
Causal classification of three Misner-type spacetimes.
Example of spacetime with causal bubbling, splitting into timelike and spacelike parts.
The paper proves a conjecture about spacetimes and singularities.
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 …
It is shown that the space of null geodesics of a causally simple Lorentzian manifold is Hausdorff if it admits an open conformal embedding into a globally hyperbolic spacetime. This provides an obstruction to conformal embeddings of causally simple spacetimes into globally hyperbolic ones irrespective of curvature con…
Study baryogenesis in conformally flat spacetimes using causal fermion systems.
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 can be conformally embedded as a…
No closed timelike geodesics in Kerr spacetimes, proving absence of closed causal geodesics.
This paper completes globally hyperbolic conformally flat spacetimes, proving they are topological manifolds.
It is shown that the space of null geodesics of a star-shaped causally simple subset of Minkowski space is contactomorphic to the canonical contact structure in the spherical cotangent bundle of . In the -dimensional case we prove a similar result for a large class of causally simple contractible subse…
Empirical evidence suggests link polynomials can detect causality in spacetimes.
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…
The paper establishes criteria for spacetime inextendibility using asymptotic volume-distance-ratio analysis.
We observe that Khovanov homology detects causality in -dimensional globally hyperbolic spacetimes whose Cauchy surface is homeomorphic to
Minimal TIP and TIF found in compact spacetimes, impacting spacetime splitting.
Study of isometries in spacetimes without observer horizons.
Note: Causality can be encoded without strict time function choice.
Globally hyperbolic spacetimes admitting infinitely many causal (and timelike) homotopy classes of curves joining two prescribed points, are exhibited and discussed.
Kerr spacetimes without closed null geodesics for non-zero rotation.
New topology defined from spacetime paths, reconstructing spacetime structure.
Continuous Lorentzian metrics yield infinitesimal Minkowskian spacetimes.
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…
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…
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.
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.
Reconstruct spacetime from order and number of points.
Generic singularities found in spacetimes with weakly trapped submanifolds.
New relation between curvature bounds and spacetime inextendibility.
Asymptotically flat static causal fermion systems are introduced. Their total mass is defined as a limit of surface layer integrals which compare the measures describing the asymptotically flat spacetime and a vacuum spacetime near spatial infinity. Our definition does not involve any regularity assumptions; it even ap…
Study examines causal properties of Finsler spacetimes with cone Killing vectors.
Detect spacetime curvature without rulers and clocks in 3D.
The paper extends completeness notions to low-regularity spacetimes.
In this work, a version of Fermat's principle for causal curves with the same energy in time orientable Finsler spacetimes is proved. We calculate the secondvariation of the {\it time arrival functional} along a geodesic in terms of the index form associated with the Finsler spacetime Lagrangian. Then the character of …
Higher-dimensional Schwarzschild spacetimes violate the Penrose property.
We show that the definition of global hyperbolicity in terms of the compactness of the causal diamonds and non-total imprisonment can be extended to spacetimes with continuous metrics, while retaining all of the equivalences to other notions of global hyperbolicity. In fact, global hyperbolicity is equivalent to the co…
Null distance encodes causal structure in spacetimes.
New calculus on spacetimes for nonlinear differential equations.
Some results related to the causality of compact Lorentzian manifolds are proven: (1) any compact Lorentzian manifold which admits a timelike conformal vector field is totally vicious, and (2) a compact Lorentzian manifold covered regularly by a globally hyperbolic spacetime admits a timelike closed geodesic, if some n…
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…
One of the central difficulties of settling the -bounded curvature conjecture for the Einstein -Vacuum equations is to be able to control the causal structure of spacetimes with such limited regularity. In this paper we show how to circumvent this difficulty by showing that the geometry of null hypersurfaces of En…