We give an up-to-date perspective with a general overview of the theory of causal properties, the derived causal structures, their classification and applications, and the definition and construction of causal boundaries and of causal symmetries, mostly for Lorentzian manifolds but also in more abstract settings.
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48 results for “causal boundary”
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…
Finslerian lightconvex boundaries: applications to causal simplicity and the space of cone geodesics math.DG
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.
Recently, the old notion of causal boundary for a spacetime V has been redefined in a consistent way. The computation of this boundary for a standard conformally stationary spacetime V = R x M, suggests a natural compactification associated to any Riemannian metric on M or, more generally, to any Fin…
We construct an example which shows that two isocausal spacetimes, in the sense introduced by García-Parrado and Senovilla, may have c-boundaries which are not equal (more precisely, not equivalent, as no bijection between the completions can preserve all the binary relations induced by causality). This example also su…
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 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.
We show that when a spacetime is globally hyperbolic with (possibly empty) smooth timelike boundary , a metrizable topology, the closed limit topology (CLT) introduced by F. Hausdorff himself in the 1950's in set theory, can be advantageously adopted on the Geroch-Kronheime…
The notion of a causal boundary for a spacetime has been a controversial topic during the last three decades. Moreover, recently the role of the boundary in the AdS/CFT correspondence for plane waves, have stimulated its redefinition with some possible alternatives. Our aim is threefold. First, to review the different …
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…
A new method selects covariates for causal effect estimation without strong assumptions.
problem Estimating causal effects without global causal structure learning and strong assumptions.
method Local covariate selection method that avoids pretreatment and causal sufficiency assumptions.
result The method achieves accurate causal effect estimation with improved computational efficiency.
FairTrade uses variational inference to create fair predictions in causal models.
problem Creating fair predictions in machine learning models with causal reasoning.
method FairTrade uses variational inference to account for unobserved confounders and integrates fairness constraints on causal paths.
result Demonstrates the effectiveness of FairTrade in creating fair predictions in both simulated and real-world datasets.
A new method reduces CI tests for causal structure learning.
problem Exponential CI tests in constraint-based methods.
method Recursive Markov boundary-based approach.
result Significantly reduces CI tests compared to existing methods.
An Adjoint-Sensitivity Framework for Lost-in-the-Middle Phenomena in Causal Residual Transformersstat.ML
Framework calculates positional influence in causal residual Transformers.
problem Understanding positional influence in causal residual Transformers.
method Adjoint-sensitivity framework for positional influence in causal residual Transformers.
result Exact evolution of adjoint-energy influence density and decomposition into residual transmission, nonlocal Volterra, and local channels.
Extends expected value framework for cost-sensitive causal decision-making.
problem Optimizing operational decision-making with cost-sensitive causal classification.
method Introduces a cost-sensitive decision boundary based on estimated individual treatment effects, positive outcome probability, and cost parameters.
result Effective in maximizing expected causal profit, outperforming cost-insensitive ranking approach.
Markov boundary improves tabular prediction but not as expected.
problem Improving tabular prediction using the Markov boundary.
method Evaluation on a synthetic SCM benchmark with feature counts from 40 to 1000.
result Restricting a regressor to the Markov boundary often improves prediction, but existing discovery and training pipelines do not fully exploit this.
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…
Globally hyperbolic spacetimes with timelike boundary are the natural class of spacetimes where regular boundary conditions (eventually asymptotic, if is obtained by means of a conformal embedding) can be posed. represents the naked singularities and c…
Causal Markov Boundariesstat.ML
Paper improves feature selection for predicting outcomes from observational data.
problem Feature selection for post-intervention outcome prediction from pre-intervention variables in healthcare settings.
method Extends Markov boundary concept to treatment-outcome pairs, uses observational and experimental data.
result Combining observational and experimental data improves feature selection and effect estimation.
We study in details the long-time asymptotic behavior of a relativistic diffusion taking values in the unitary tangent bundle of a curved Lorentzian manifold, namely a spatially flat and fast expanding Robertson-Walker space-time. We prove in particular that the Poisson boundary of the diffusion can be identified with …
Establishes a version of Bartnik's conjecture for Lorentzian length spaces.
problem Proving Bartnik's conjecture for Lorentzian length spaces.
method Using timelike completeness and non-negative timelike curvature bounds, the causal boundary is shown to be a single point.
result A globally hyperbolic Lorentzian length space splits as a metric Lorentzian product.
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].
We consider the future causal boundary as a tool to find obstructions to conformal extensions, the latter being a slight generalization to conformal compactifications.
Ridge regularized linear models (RRLMs), such as ridge regression and the SVM, are a popular group of methods that are used in conjunction with coefficient hypothesis testing to discover explanatory variables with a significant multivariate association to a response. However, many investigators are reluctant to draw ca…
We prove that the topology, smooth structure, and metric of a compact Lorentzian manifold with boundary is uniquely determined by data at the boundary. The data consists of the lengths and directions of future-directed once-broken geodesics connecting points on the boundary, which are first timelike and then lightlike.…
Study Gromov hyperbolic domains in Minkowski space, proving equivalence to boundary properties.
problem Investigate Gromov hyperbolic domains in Minkowski space.
method Explicit comparisons between metrics, dynamical arguments, and quasi-hyperbolic metric.
result Gromov hyperbolicity of convex, future complete domains is equivalent to stable acausality of the boundary.
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…
Transportability without Graphs: A Bayesian Approach to Identifying s-Admissible Backdoor Setsstat.ML
Bayesian method identifies causal sets across populations without graph knowledge.
problem Transporting causal information across populations without causal graph knowledge.
method Combines observational and experimental data to identify s-admissible backdoor sets.
result Proves asymptotic convergence and corrects transportability bias in simulations.
We give new definitions of null infinity and black hole in terms of causal boundaries, applicable to any strongly causal spacetime . These are meant to extend the standard ones given in terms of conformal boundaries, and use the new definitions to prove a classic result in black hole theory for this more general…
Wave equation map reveals manifold's structure.
problem Reconstructing Lorentzian manifold from wave equation map.
method Analyzing Schwartz kernel and boundary light observation set.
result Full Lorentzian structure can be recovered under geometric assumptions.
Study on merging predictors in causal and anticausal directions using CMAXENT.
problem Comparing merging predictors in causal and anticausal directions.
method Using CMAXENT as inductive bias, study differences in merging predictors.
result CMAXENT solution reduces to logistic regression in causal direction and LDA in anticausal direction.
We study smooth {\sf traversing} vector fields on compact manifolds with boundary. A traversing admits a Lyapunov function such that . We show that the trajectory spaces of {\sf traversally generic} -flows are {\sf Whitney stratified spaces}, and thus admit tr…
Study open orbits in causal flag manifolds with applications in AQFT.
problem Understanding open orbits in causal flag manifolds for applications in AQFT.
method Analyzing open orbits of symmetric subgroups on causal flag manifolds, focusing on invariant causal structures and modular flows.
result Determine the positivity regions of modular flows and their global hyperbolicity for different types of open orbits.
CDFM aims to unify causal discovery across diverse datasets.
problem Fragmented, test-driven causal discovery approaches struggle with modern data heterogeneity.
method CDFM is a unified, general-purpose framework using a variational decomposition of causal mechanisms.
result CDFM outperforms traditional algorithms across diverse datasets.
Recently, a new viewpoint on the classical c-boundary in Mathematical Relativity has been developed, the relations of this boundary with the conformal one and other classical boundaries have been analyzed, and its computation in some classes of spacetimes, as the standard stationary ones, has been carried out. In the p…
The paper is concerned with regularity properties of boundaries of causal pasts of points in a 3+1-dimensional Einstein-vacuum spacetime. In a Lorentzian manifold such boundaries play crucial role in propagation of linear and nonlinear waves. We prove a uniform lower bound on the radius of injectivity of these null bou…
Study subgroups preserving proper domains in flag manifolds.
problem Identify subgroups preserving proper domains in flag manifolds.
method Establish necessary conditions and introduce causal convexity in Shilov boundary.
result Transverse subgroups with geometric properties in Shilov boundary.
Defines timelike ideal boundary for non-positively curved Lorentzian spaces.
problem Understanding the geometry of non-positively curved Lorentzian spaces.
method Introduces timelike ideal boundary as asymptotic classes of geodesic rays, endows with topology and metric, and studies upper curvature bounds.
result Established upper curvature bounds for the resulting metric space.
New fairness criteria for algorithmic recourse actions that consider causal relationships.
problem Fairness of recourse actions in algorithmic classification.
method Proposes two new fairness criteria at group and individual levels, explicitly accounting for causal relationships.
result Fairness of recourse is complementary to fairness of prediction, and can be enforced by altering the classifier.
New concept of Lorentzian-Euclidean black holes and metric transitions explored.
problem Signature-changing spacetimes and their geometric properties.
method Introduction and analysis of Lorentzian-Euclidean black holes and transitions.
result Consistency of proper time to horizon in Lorentzian-Euclidean black holes.
We study the causality relation in the 3-dimensional anti-de Sitter space AdS and its conformal boundary Ein. To any closed achronal subset in we associate the invisible domain from in AdS. We show that if is a torsion-free discrete group of isometries of AdS preserving and is non-elem…
Proposes a new model for online anomaly detection in multivariate time series.
problem Inaccurate anomaly detection in multivariate time series due to spurious correlations and lack of temporal causality.
method Clusters channels based on correlations, embeds each cluster, and integrates information through a causal mixer while maintaining temporal causality.
result Consistently superior performance across six public benchmark datasets.
Proposes a new method for algorithmic recourse in confounded settings.
problem Provides actionable recommendations for individuals affected by automated decisions.
method Relaxes assumptions of no hidden confounding and additive noise, requiring only causal graph and confounding structure.
result Bounds the expected counterfactual effect of recourse actions, ensuring favourable outcomes in expectation.
In this paper, we determine the Poisson boundary of the relativistic Brownian motion in two classes of Lorentzian manifolds, namely model manifolds of constant scalar curvature and Robertson--Walker space-times, the latter constituting a large family of curved manifolds. Our objective is two fold: on the one hand, to u…
Recourse explanations can become invalid if collective actions change statistical data.
problem Recourse explanations may become invalid due to collective behavior changing data statistics.
method Formal characterization of conditions under which recourse explanations remain valid under performativity.
result Recourse actions may become invalid if they are influenced by or intervene on non-causal variables.
In this paper, we parametrize the space of isometric immersions of the hyperbolic plane into the hyperbolic 3-space in terms of null-causal curves in the space of oriented geodesics. Moreover, we characterize "ideal cones" (i.e., cones whose vertices are on the ideal boundary) by behavior of their mean curvature.
By using Stationary-to-Randers correspondence (SRC), a characterization of light and time-convexity of the boundary of a region of a standard stationary (n+1)-spacetime is obtained, in terms of the convexity of the boundary of a domain in a Finsler n or (n+1)-space of Randers type. The latter convexity is analyzed in d…
Lightlike hypersurfaces in cone structures minimize time.
problem Finding time-minimizing paths in cone structures.
method Defining lightlike hypersurfaces and proving their foliation by cone geodesics.
result Lightlike hypersurfaces in globally hyperbolic spacetimes are time-minimizing.