arXiv research

Maximal causal curves for Lipschitz metrics are either lightlike or timelike.

The Abstract Boundary singularity theorem was first proven by Ashley and Scott. It links the existence of incomplete causal geodesics in strongly causal, maximally extended spacetimes to the existence of Abstract Boundary essential singularities, i.e., non-removable singular boundary points. We give two generalizations…

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…

Proves Gannon-Lee theorem for $C^1$ spacetimes.

The study of low regularity (in-)extendibility of Lorentzian manifolds is motivated by the question whether a given solution to the Einstein equations can be extended (or is maximal) as a weak solution. In this paper we show that a timelike complete and globally hyperbolic Lorentzian manifold is $C^0$-inextendible. For…

We introduce a version of Aubry-Mather theory for the length functional of causal curves in compact Lorentzian manifolds. Results include the existence of maximal invariant measures, calibrations and calibrated curves. We prove two versions of the Mather's graph theorem. A class of examples, the Lorentzian Hedlund exam…

Irrespective of local conditions imposed on the metric, any extendible spacetime U has a maximal extension containing no closed causal curves outside the chronological past of U. We prove this fact and interpret it as impossibility (in classical general relativity) of the time machines, insofar as the latter are define…

Recent results on the maximization of the charged-particle action I in a globally hyperbolic spacetime are discussed and generalized. We focus on the maximization of I over a given causal homotopy class C of curves connecting two causally related events x_0 <= x_1. Action I is proved to admit a maximum on C, and also o…

Defines new metrics for Lorentzian spaces and their convergence.

Causality violations are typically seen as unrealistic and undesirable features of a physical model. The following points out three reasons why causality violations, which Bonnor and Steadman identified even in solutions to the Einstein equation referring to ordinary laboratory situations, are not necessarily undesirab…

Let $(M,g)$ be a time oriented Lorentzian manifold and $d$ the Lorentzian distance on $M$. The function $τ(q):=\sup_{p< q} d(p,q)$ is the cosmological time function of $M$, where as usual $p< q$ means that $p$ is in the causal past of $q$. This function is called regular iff $τ(q) < \infty$ for all $q$ and also $τ\to 0…

We demonstrate the breakdown of several fundamentals of Lorentzian causality theory in low regularity. Most notably, chronological futures (defined naturally using locally Lipschitz curves) may be non-open, and may differ from the corresponding sets defined via piecewise $C^1$-curves. By refining the notion of a causal…

Proposes a new method to optimize treatment allocation with budget constraints.

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…

Researchers examine various causal structures for spacetimes with continuous metrics.

Paper tackles estimating individual treatment effects from observational data.

A new framework learns cyclic causal graphs from incomplete data.

New kernel methods estimate complex causal relationships.

MissNODAG learns cyclic causal graphs from incomplete data.

The paper introduces revenue uplift modeling to maximize marketing profits.

Framework detects and mitigates data-poisoning attacks in causal effect estimation.

Extends expected value framework for cost-sensitive causal decision-making.

The paper classifies maximal translation surfaces in Lorentz-Minkowski space.

We establish that over a C^{2,1} manifold the exponential map of any Lipschitz connection or spray determines a local Lipeomophism and that, furthermore, reversible convex normal neighborhoods do exist. To that end we use the method of Picard-Lindelof approximation to prove the strong differentiability of the exponenti…

RECLAIM discovers causal graphs in cyclic, noisy systems.

Optimization algorithm CoCo improves causal inference from diverse data.

Study fairness in intervention to maximize outcomes.

Globally hyperbolic spacetimes admitting infinitely many causal (and timelike) homotopy classes of curves joining two prescribed points, are exhibited and discussed.

DCEM algorithm reduces bias in machine learning models trained on selective labels.

Unique maximal curve systems found for up to 5 punctures.

Torically maximal curves (known also as simple Harnack curves) are real algebraic curves in the projective plane such that their logarithmic Gauß map is totally real. In this paper we show that hyperplanes in projective spaces are the only torically maximal hypersurfaces of higher dimensions.

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…

DEBIAS learns causal effects from psychiatric longitudinal data by optimizing outcome weights.

We formulate certain inequalities for the geometric quantities characterizing causal diamonds in curved and Minkowski spacetimes. These inequalities involve the red-shift factor which, as we show explicitly in the spherically symmetric case, is monotonic in the radial direction and it takes its maximal value at the cen…

Kerr spacetimes without closed null geodesics for non-zero rotation.

ContiVAE estimates individual dose-response curves from unobserved confounders using observational data.

Based on the recent work \cite{PII} we put forward a new type of transformation for Lorentzian manifolds characterized by mapping every causal future-directed vector onto a causal future-directed vector. The set of all such transformations, which we call causal symmetries, has the structure of a submonoid which contain…

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…

We classify closed, simply-connected, non-negatively curved 6-manifolds of almost maximal symmetry rank up to equivariant diffeomorphism.

New algorithm improves causal effect estimation for continuous treatments.

Develops methods for making deep learning models more interpretable by answering counterfactual questions.

Causal KL improves on existing metrics for evaluating causal models.

Efficient algorithm for identifying causal effects in linear models.

A reconstruction theorem in terms of the topology and geometrical structures on the spaces of light rays and skies of a given space-time is discussed. This result can be seen as part of Penrose and Low's programme intending to describe the causal structure of a space-time $M$ in terms of the topological and geometrical…

The notion of maximal extension of a globally hyperbolic space-time arises from the notion of maximal solutions of the Cauchy problem associated to the Einstein's equations of general relativity. In 1969 Choquet-Bruhat and Geroch proved that if the Cauchy problem has a local solution, this solution has a unique maximal…

Interpolates curves using maximal and minimal surfaces in different spaces.

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 …

Researchers solve a Plateau problem for maximal surfaces in pseudo-hyperbolic spaces.