The abstract discusses topological censorship with five hypotheses.
problem Proving topological censorship in spacetimes.
method Presented five hypotheses to prove a theorem.
result Proof of a topological censorship theorem.
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The study proves strong cosmic censorship violation for spherically symmetric dust clouds.
problem Violation of strong cosmic censorship for spherically symmetric dust clouds.
method Derived an ordinary differential equation for light rays and used it to prove strong cosmic censorship violation.
result Generic violation of strong cosmic censorship for spherically symmetric dust clouds.
DCEM algorithm reduces bias in machine learning models trained on selective labels.
problem Bias in machine learning models trained on selective labels.
method Disparate Censorship Expectation-Maximization (DCEM) algorithm.
result DCEM improves bias mitigation without sacrificing discriminative performance.
Strong cosmic censorship for surface-symmetric cosmological spacetimes with collisionless mattergr-qc
This paper addresses strong cosmic censorship for spacetimes with self-gravitating collisionless matter, evolving from surface-symmetric compact initial data. The global dynamics exhibit qualitatively different features according to the sign of the curvature of the symmetric surfaces and the cosmological constant $…
Proves weak cosmic censorship for a specific Einstein-scalar field system in 2+1 dimensions.
problem Proves the absence of naked singularities in a specific Einstein-scalar field system.
method Establishes a mass gap and shows the presence of infinite blueshift to prove the absence of naked singularities.
result Proves the weak cosmic censorship conjecture for the circularly symmetric Einstein-scalar field system in 2+1 dimensions.
Theorem proves topological censorship for universes with positive cosmological constant.
problem Proving topological censorship for spacetimes with positive cosmological constant.
method Developed a new theorem assuming eventual isolation of black hole collections.
result Regions near black hole collections have trivial fundamental group.
Study compares machine learning and econometric models for demand prediction with and without accounting for sales censorship.
problem Predicting demand based on sales data and correcting bias in estimates of demand parameters.
method Constructed two ensemble models: one accounting for sales censorship and one not. Used censored quantile regression and various machine learning models.
result Machine learning models with censorship accounting provide similar bias-corrected demand sensitivity estimates as econometric models.
Study bandit problems under censorship, estimating performance loss.
problem Estimating performance loss in bandit problems with censored feedback.
method Introduced a broad class of censorship models and analyzed their effective dimension.
result Effective dimension naturally leads to results analogous to uncensored settings.
Penrose's conjecture links black holes and gravitational singularities.
problem Deterministic nature of General Relativity and black holes.
method Modern techniques in partial differential equations applied to gravitational collapse.
result Recent advances in understanding Strong Cosmic Censorship.
The paper addresses supervised learning with censored data, proposing a method to estimate risk.
problem Learning from censored data in regression problems.
method Proposes a plug-in estimate of the true risk based on a Kaplan-Meier estimator of the censorship distribution.
result The learning rate of minimizers of the proposed risk functional is of order \(O_{\mathbb{P}}(\sqrt{\log(n)/n})\).
Proposes a weaker version of Strong Cosmic Censorship with curvature bounds.
problem The original Strong Cosmic Censorship conjecture.
method Weakens the conjecture to allow manifolds with bounded curvature and Lipschitz continuity of metrics.
result Proves the conjecture with bounded curvature for sufficiently large p (p>4 with uniform bounds, p>2 without uniform bounds).
Deep Recurrent Survival Analysis models for better event prediction and survival rate estimation.
problem Survival analysis challenges in handling data censorship and sequential patterns.
method Combines deep learning for conditional probability prediction and survival analysis for censorship handling.
result Significantly outperforms state-of-the-art solutions in various metrics on real-world tasks.
Study on black hole interiors with matter fields, showing oscillation condition impacts blow-up.
problem Examining Strong Cosmic Censorship in the presence of matter fields.
method Einstein equations coupled with charged/massive scalar fields, spherically symmetric data, relaxation rate analysis.
result Oscillation condition on event horizon determines whether matter fields blow up or not.
We address the issue of strong cosmic censorship for T^2-symmetric spacetimes with positive cosmological constant. In the case of collisionless matter, we complete the proof of the C^2 formulation of the conjecture for this class of spacetimes. In the vacuum case, we prove that the conjecture holds for the special case…
Proof confirms cosmic censorship for charged gravitational collapse.
problem Cosmic censorship for Einstein-Maxwell-Charged Scalar Field system.
method Systematic approach to incorporate charge and complex scalar field, new trapped surface criterion, modified BV area estimates, and new instability theorems.
result Cosmic censorship holds for charged gravitational collapse.
It is observed that on many 4-manifolds there is a unique smooth structure underlying a globally hyperbolic Lorentz metric. For instance, every contractible smooth 4-manifold admitting a globally hyperbolic Lorentz metric is diffeomorphic to the standard . Similarly, a smooth 4-manifold homeomorphic to the produc…
New data shows multiple black holes can form from modified vacuum data.
problem Formation of multiple black holes from modified vacuum data.
method Modified Brill-Lindquist metric, short-pulse framework, stability analysis, gluing method.
result Formation of multiple black holes in finite time under weak cosmic censorship.
The Strong Cosmic Censorship conjecture states that for generic initial data to Einstein's field equations, the maximal globally hyperbolic development is inextendible. We prove this conjecture in the class of orthogonal Bianchi class B perfect fluids and vacuum spacetimes, by showing that unboundedness of certain curv…
Study on naked singularities without symmetry, forming incomplete future null infinity and singular inner Cauchy horizon.
problem Formation of naked singularities in Einstein-scalar field system without symmetry assumptions.
method Employing four-type differences and scale-invariant weighted norms to control geometry.
result Global naked singularity structure with incomplete future null infinity and singular inner Cauchy horizon.
Proves conditions for Cauchy horizons in low-regularity spacetimes.
problem Conditions for the existence of Cauchy horizons in spacetimes with low regularity.
method Analyzes the relationship between complete Cauchy hypersurfaces, almost closed causal curves, and points at infinity.
result Wald's conjecture reformulated as a PDE problem about Cauchy horizons.
SurvCaus improves survival CATE estimation using neural nets.
problem Estimating Individual Treatment Effects (ITE) in survival analysis.
method Representation balancing for counterfactual inference with neural networks.
result The proposed method outperforms baseline methods in synthetic and semisynthetic datasets.
The paper connects Diophantine approximation to black hole behavior, proving blow-up conditions.
problem Understanding the behavior of waves on Kerr-AdS black holes.
method Analyzing linear scalar perturbations and studying poles of the interior scattering operator.
result Perturbations blow up at the Cauchy horizon under certain non-Diophantine conditions.
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.
In the first part of this work we show a uniqueness result for globally hyperbolic spacetimes with a spacelike conformal boundary satisfying the vacuum Einstein equations with positive cosmological constant. Then we present applications of this result in the contexts of cosmic censorship and the initial value problem i…
Modeling shared mobility demand considering supply limitations.
problem Inaccurate demand predictions due to limited supply.
method Censored Gaussian Processes for demand modeling.
result Taking supply limitations into account improves demand predictions.
We introduce a natural generalization of marginally outer trapped surfaces, called immersed marginally outer trapped surfaces, and prove that three dimensional asymptotically flat initial data sets either contain such surfaces or are diffeomorphic to R^3. We establish a generalization of the Penrose singularity theorem…
New method proves instability of naked singularity and censors it.
problem Proving instability and censoring naked singularity.
method Einstein-scalar field system, hyperbolic short-pulse method, non-perturbative elliptic arguments.
result Tiny anisotropic perturbation leads to anisotropic apparent horizon censoring the naked singularity.
Proves inextendibility of weak null singularities from curvature blow-up.
problem Inextendibility of weak null singularities in the context of curvature blow-up.
method Introduces a new strategy to infer -inextendibility from curvature blow-up.
result Expected to contribute to the resolution of strong cosmic censorship conjecture.
We initiate a series of works where we study the interior of dynamical rotating vacuum black holes without symmetry. In the present paper, we take up the problem starting from appropriate Cauchy data for the Einstein vacuum equations defined on a hypersurface already within the black hole interior, representing the exp…
Proves existence of Killing fields in smooth spacetimes with compact Cauchy horizons.
problem Existence of Killing fields in smooth spacetimes with compact Cauchy horizons.
method Normalized surface gravity of compact non-degenerate Cauchy horizons in smooth vacuum spacetimes.
result Proves the Isenberg-Moncrief conjecture on the existence of Killing fields.
Symmetries of vacuum spacetimes with a compact Cauchy horizon of constant non-zero surface gravitymath.DG
Proves symmetry in vacuum spacetimes with compact Cauchy horizons.
problem Symmetries in vacuum spacetimes with compact Cauchy horizons.
method Solving Killing equation up to infinite order at the Cauchy horizon, extending the solution to the globally hyperbolic region.
result Maximally globally hyperbolic vacuum development cannot be extended across compact Cauchy horizons.
The paper examines gravitational singularities in spacetimes and proves inextendibility.
problem Investigating gravitational singularities in spacetimes.
method Analyzing local holonomy and using it to prove inextendibility.
result Proves the -inextendibility of certain spacetimes.
New taxonomy reveals different detection limits for various types of fraud.
problem Existing fraud detection treats all fraud as the same, ignoring its diverse forms.
method Introduced an observation-mechanism taxonomy with five fraud classes.
result Separate estimation by fraud class outperforms pooled estimation.
Researchers use conformal infinity to study spacetimes near AdS2×S2.
problem Studying the rigidity of asymptotically AdS2×S2 spacetimes.
method Developed a new approach based on conformal infinity.
result Obtained new results including similar to [4] but for higher dimensions and more than two ends.
For almost half of the one hundred year history of Einstein's theory of general relativity, Strong Cosmic Censorship has been one of its most intriguing conjectures. The SCC conjecture addresses the issue of the nature of the singularities found in most solutions of Einstein's gravitational field equations: Are such si…
The intention of this article is to give a flavour of some global problems in General Relativity. We cover a variety of topics, some of them related to the fundamental concept of 'Cauchy hypersurfaces': (1) structure of globally hyperbolic spacetimes, (2) the relativistic initial value problem, (3) constant mean curvat…
Rough initial data and the strength of the blue-shift instability on cosmological black holes with gr-qc
We consider the wave equation on Reissner-Nordström-de Sitter and more generally Kerr-Newman-de Sitter black hole spacetimes with . The strength of the blue-shift instability associated to the Cauchy horizon of these spacetimes has been the subject of much discussion, since-in contrast to the case-the compet…
We initiate the mathematical study of spherical collapse of self-gravitating charged scalar fields. The main result gives a complete characterization of the future boundary of spacetime, providing a starting point for studying the cosmic censorship conjectures. In general, the boundary includes two null components, one…
Motivated by the cosmic censorship conjecture in mathematical relativity, we establish the precise mass lower bound for an asymptotically flat Riemannian 3-manifold with nonnegative scalar curvature and minimal surface boundary, in terms of angular momentum and charge. In particular this result does not require the res…
We use the inverse mean curvature flow to establish Penrose-type inequalities for time-symmetric Einstein-Maxwell initial data sets which can be suitably embedded as a hypersurface in Euclidean space , . In particular, we prove a positive mass theorem for this class of charged black holes. As …
Paper proves existence of anisotropic dynamical horizons in gravitational collapse.
problem Existence of apparent horizons in gravitational collapse.
method Scale-critical hyperbolic method and non-perturbative elliptic techniques.
result Smooth and spacelike apparent horizons emerge from general initial data in gravitational collapse.
We note an area-charge inequality orignially due to Gibbons: if the outermost horizon in an asymptotically flat electrovacuum initial data set is connected then , where is the total charge and is the area radius of . A consequence of this inequality is that for connected black hole…
The paper proves the existence of Ricci-flat metrics on certain exotic 4-manifolds.
problem Proving the existence of Ricci-flat metrics on exotic 4-manifolds.
method Constructing Ricci-flat metrics on Gompf's exotic 4-manifolds.
result Proves the existence of complete Ricci-flat metrics on certain exotic 4-manifolds.
We prove that a large class of smooth solutions to the linear wave equation on subextremal rotating Kerr spacetimes which are regular and decaying along the event horizon become singular at the Cauchy horizon. More precisely, we show that assuming appropriate upper and lower bounds on the energy along t…
Paper proposes efficient algorithm for recovering sparsity pattern from deterministic missing data.
problem Recovering sparsity pattern from datasets with deterministic missing structure.
method Proposes an efficient algorithm for missing value imputation using topological property of censorship filter.
result Consistently recovers the sparsity pattern with high probability in polynomial time and logarithmic sample complexity.
Scalar-tensor gravitation theories, such as the Brans-Dicke family of theories, are commonly partly described by a modified Einstein equation in which the Ricci tensor is replaced by the Bakry-Émery-Ricci tensor of a Lorentzian metric and scalar field. In physics this formulation is sometimes referred to as the "Jordan…
We develop a model to cluster time-series data with interval censoring, improving disease phenotyping.
problem Noise and interval censoring hinder clustering in disease phenotyping.
method Deep generative, continuous-time model that clusters time-series data while correcting for censorship.
result Our model corrects for interval censoring and recovers known clinical subtypes.
GPI uses GenAI models to infer causal and predictive effects from unstructured data.
problem Estimating causal and predictive effects from unstructured data like text and images.
method Leverages open-source GenAI models to generate and represent unstructured data, applying machine learning to these representations.
result GPI efficiently estimates causal and predictive effects with quantified uncertainty, without fine-tuning.