New counterexamples found to cosmic censor conjecture in 4D.
problem Cosmic censor conjecture in 4D physics.
method Constructing non-globally hyperbolic Lorentzian 4-manifolds using exotic and self-dual spaces.
result Found physical counterexamples to the strong cosmic censor conjecture.
In this letter a generic counterexample to the strong cosmic censor conjecture is exhibited. More precisely---taking into account that the conjecture lacks any precise formulation yet---first we make sense of what one would mean by a "generic counterexample" by introducing the mathematically unambigous and logically st…
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 ψ blow up at the Cauchy horizon under certain non-Diophantine conditions. 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 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.
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).
Study proves cosmic no-hair conjecture for certain spacetimes.
problem Proving cosmic no-hair conjecture for T2-symmetric spacetimes.
method Analyzing Einstein non-linear scalar field equations with T2-symmetry.
result Future causal geodesic completeness and cosmic no-hair proved.
Proves Strong Cosmic Censorship conjecture for specific spacetimes.
problem Proving the Strong Cosmic Censorship conjecture for certain spacetimes.
method Analyzing curvature invariants and expansion-normalised variables.
result Proven for orthogonal Bianchi class B perfect fluids and vacuum spacetimes.
Study geometric properties of generalized vacuum static spaces.
problem Estimating geometric properties of generalized φ-vacuum static spaces. method Proving estimates for φ-scalar curvature and first eigenvalue of the Jacobi operator, and rigidity under various geometric assumptions. result Proved a result related to the Cosmic no-hair conjecture.
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…
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.
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.
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.
The article characterizes a hemisphere using a Laplace operator and a differential equation.
problem Characterizing a hemisphere in a Riemannian manifold with boundary.
method Using the de-Rham Laplace operator and a nontrivial solution of the Fischer-Marsden equation.
result Proves the cosmic no-hair conjecture under a given integral condition.
Study on static perfect fluid space-time geometry and boundary estimates.
problem Investigate the geometry and boundary properties of static perfect fluid space-time.
method Used generalized Reilly's formula to establish geometric inequalities and boundary estimates.
result Obtained new boundary estimates involving the Brown-York mass and first eigenvalue of the Jacobi operator.
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.
Study finds mass bound for 3-manifolds with boundary, angular momentum, and charge.
problem Establishing precise mass lower bound for asymptotically flat 3-manifolds.
method Analyzes nonnegative scalar curvature and minimal surface boundary conditions, without simple connectivity and completeness.
result Proves mass lower bound in terms of angular momentum and charge, without restrictive assumptions.
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…
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.
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.
The study characterizes Riemannian manifolds with conformal vector fields and proves isometric properties.
problem Characterizing Riemannian manifolds with conformal vector fields and boundary conditions.
method Analyzing the properties of conformal vector fields on compact Riemannian manifolds with or without boundary.
result Proves isometric properties of Riemannian manifolds under specific conditions.
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 Cloc0,1-inextendibility from curvature blow-up. result Expected to contribute to the resolution of strong cosmic censorship conjecture.
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.
Study cosmic structures using Topological Data Analysis and Persistence Energy.
problem Investigate cosmic web evolution in ΛCDM cosmologies. method Apply LITE method to embed persistence diagrams into vector spaces and analyze cosmic structures.
result Discover a correlation between Persistence Energy and redshift values.
Paper uses ResUNet-CMB to reconstruct cosmic polarization rotation from CMB data.
problem Reconstructing anisotropic cosmic polarization rotation from CMB data.
method Extended ResUNet-CMB to handle gravitational lensing and patchy reionization.
result ResUNet-CMB outperforms standard quadratic estimator in reconstructing all three effects.
Study of mean curvature flow in de Sitter space, showing convergence to flat slicing.
problem Mean curvature flow in de Sitter space.
method Analysis of mean convex mean curvature flow of local spacelike graphs in de Sitter space.
result As s goes to infinity, Ms becomes graphical in expanding balls, converging to the flat slicing of de Sitter space. Paper proves instability of naked singularities in spherical symmetry without contradiction.
problem Stability of naked singularities in spherical symmetry of self-gravitating scalar fields.
method Appropriate a priori estimates for the solution, relaxing original sharp estimates.
result Robust argument proving instability without contradiction.
Study on the interior of rotating vacuum black holes, proving stability of Cauchy horizon.
problem Stability of Cauchy horizon in rotating vacuum black holes.
method Maximal Cauchy evolution extension across non-trivial piece of Cauchy horizon.
result Continuous metric Cauchy horizon can be extended across a non-trivial piece of Cauchy horizon.
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.
Tree-based machine learning detects cosmic strings in CMB maps.
problem Detecting cosmic strings in CMB maps.
method Random forest and gradient boosting algorithms.
result Improved detection of cosmic strings with Gμ≳3.0imes10−8. 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.
In this work we consider the gravitating vortex equations. These equations couple a metric over a compact Riemann surface with a hermitian metric over a holomorphic line bundle equipped with a fixed global section --- the Higgs field ---, and have a symplectic interpretation as moment-map equations. As a particular cas…
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 Rn+1, n≥3. In particular, we prove a positive mass theorem for this class of charged black holes. As …
GANs generate realistic cosmic web models in seconds, overcoming computational limits.
problem Resource-intensive N-body simulations limit upcoming cosmology experiments.
method Generative Adversarial Networks (GANs) trained on 2D snapshots of N-body simulations.
result GAN-generated cosmic web models are qualitatively and quantitatively similar to originals.
New model reduces bias in cosmic shear measurements.
problem Bias in cosmic shear measurements due to non-well-defined ellipticity.
method Hybrid physical and deep learning Hierarchical Bayesian Model.
result Unbiased estimate of shear on realistic galaxies.
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 k of the symmetric surfaces and the cosmological constant $…
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.
This paper addresses issues with the Brier score in administrative censoring scenarios.
problem Problems with the Brier score in administrative censoring scenarios.
method Proposes an alternative Brier score for administratively censored data.
result The administrative Brier score is valid even when censoring times can be identified from covariates.
We prove that a large class of smooth solutions ψ to the linear wave equation □gψ=0 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…
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…
We consider how microlocal methods developed for tomographic problems can be used to detect singularities of the Lorentzian metric of the Universe using measurements of the Cosmic Microwave Background radiation. The physical model we study is mathematically rigorous but highly idealized.
We study Jang's equation on a one-parameter family of asymptotically flat, spherically symmetric Cauchy hypersurfaces in the maximally extended Schwarzschild spacetime. The hypersurfaces contain apparent horizons and are parametrized by their proximity to the singularity at r=0. We show that on those hypersurfaces …
This research connects topological changes to cosmic phenomena like black hole formation.
problem Understanding topological changes in cosmic phenomena.
method Using topological surgery and Morse functions to describe changes in 3-manifolds and their fundamental groups.
result New insights into natural phenomena through a topological perspective.
A new boosting model handles dependent censoring in time-to-event data.
problem Independent censoring assumption leads to biased predictions in time-to-event analysis.
method Clayton-boost, a boosting approach using Clayton copula.
result Clayton-boost outperforms other methods in handling dependent censoring.
The maximal analytic Schwarzschild spacetime is manifestly inextendible as a Lorentzian manifold with a twice continuously differentiable metric. In this paper, we prove the stronger statement that it is even inextendible as a Lorentzian manifold with a continuous metric. To capture the obstruction to continuous extens…
Simplified proof of cosmic singularity theorem using new mathematical techniques.
problem Proving cosmic singularity in expanding spacetimes with positive cosmological constant.
method Unified approach using the positive resolution of the virtual positive first Betti number conjecture.
result The theorem holds without the need for a spherical Cauchy surface.
Develops a method to estimate quantiles in censored data using random forests.
problem Inability of random forests to handle censored data, leading to poor predictive performance.
method Censored Quantile Regression Forests (CQRF) based on local adaptive random forests.
result Consistent estimation of quantiles without parametric modeling assumptions.
Develops a method to estimate quantiles in censored data using random forests.
problem Inability of random forests to handle randomly censored observations.
method Regression adjustment for quantile regression models based on a new estimating equation.
result Consistent estimation of quantiles without parametric modeling assumptions.