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.
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.
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. We consider spacetimes solving the Einstein non-linear scalar field equations with T2-symmetry and show that they admit an areal time foliation in the expanding direction. In particular, we prove global existence and uniqueness of solutions to the corresponding system of evolution equations for all future times. The on…
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.
Geodesic balls in a simply connected space forms Sn, Rn or Hn are distinguished manifolds for comparison in bounded Riemannian geometry. In this paper we show that they have the maximum possible boundary volume among Miao-Tam critical metrics with connected boundary provided that…
Proves no-hair theorem for certain vacuum black holes.
problem No-hair theorem for stationary vacuum black holes.
method Proof of no-hair theorem, definition of surface gravity and angular velocity, analysis of near-horizon geometries.
result Completion of no-hair theorem proof for specified black holes.
The paper studies φ-static perfect fluid space-times in Einstein's General Relativity.
problem Analyzing the geometry of φ-static perfect fluid space-times. method Reduction of Einstein's Field Equations to the factors of a static warped product, introducing φ-curvatures. result Sharp sufficient conditions for a compact φ-SPFST with boundary to be isometric to the standard hemisphere. Automates hair color digitization using imaging and deep learning.
problem Challenges in capturing and rendering realistic hair colors.
method Combines imaging, path-tracing, and self-supervised machine learning.
result Accurately captures and renders hair color with synthetic images.
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).
In a previous paper we obtained formulae for the volume of a causal diamond or Alexandrov open set I+(p)∩I−(q) whose duration τ(p,q) is short compared with the curvature scale. In the present paper we obtain asymptotic formulae valid when the point q recedes to the future boundary I+ of an asymp…
This work introduces 'Artificial Entanglement' to understand LLMs' fine-tuning effectiveness.
problem Understanding the effectiveness of parameter-efficient fine-tuning methods for large language models.
method Adopting a quantum-information-inspired perspective, the study measures 'Artificial Entanglement' in neural networks.
result LoRA and FFT induce distinct internal entanglement signatures but not external ones, suggesting a 'no-hair' property.
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.
Kricker constructed a knot invariant Z^{rat} valued in a space of Feynman diagrams with beads. When composed with the so called "hair" map H, it gives the Kontsevich integral of the knot. We introduce a new grading on diagrams with beads and use it to show that a non trivial element constructed from Vogel's zero diviso…
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.
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.
We uniquely and explicitly reconstruct the instantaneous intrinsic metric of the Kerr-Newman Event Horizon from the spectrum of its Laplacian. In the process we find that the angular momentum parameter, radius, area; and in the uncharged case, mass, can be written in terms of these eigenvalues. In the uncharged case th…
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 $…
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 explore the use of random forest and gradient boosting, two powerful tree-based machine learning algorithms, for the detection of cosmic strings in maps of the cosmic microwave background (CMB), through their unique Gott-Kaiser-Stebbins effect on the temperature anisotropies.The information in the maps is compressed…
Dark matter in the universe evolves through gravity to form a complex network of halos, filaments, sheets and voids, that is known as the cosmic web. Computational models of the underlying physical processes, such as classical N-body simulations, are extremely resource intensive, as they track the action of gravity in …
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.
Study on spin random fields using chaos decomposition for cosmic microwave background modeling.
problem Modeling polarization of Cosmic Microwave Background using spin random fields.
method Explicit Wiener-Itô chaos decomposition of area measures of level sets.
result Reveals a clear difference between high frequency regime and zero spin case.
The large-scale structure of the universe is comprised of virialized blob-like clusters, linear filaments, sheet-like walls and huge near empty three-dimensional voids. Characterizing the large scale universe is essential to our understanding of the formation and evolution of galaxies. The density range of clusters, wa…
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…
Recent work shows unequal performance of commercial face classification services in the gender classification task across intersectional groups defined by skin type and gender. Accuracy on dark-skinned females is significantly worse than on any other group. In this paper, we conduct several analyses to try to uncover t…
Bayesian neural networks improve cosmic parameter estimation from modified gravity simulations.
problem Estimating cosmological parameters from large-scale structure data with modified gravity.
method Implement Bayesian neural networks (BNNs) with two cases: single BLL and FullB, trained on dark matter only particle mesh N-body simulations. result BNNs yield well-calibrated uncertainty estimates and accurately predict cosmological parameters for Ωm and σ8. CoSMIC extends flow-based SVI to transdimensional problems.
problem Bayesian structure learning and model selection with multi-model parameter spaces.
method Normalizing flows with a combined stochastic variational transdimensional inference approach.
result Improved performance on high-cardinality model spaces.
Study shows how 3+1D cosmologies can evolve to de Sitter space under certain conditions.
problem Understanding the evolution of 3+1D cosmologies with specific symmetry constraints.
method Mean Curvature Flow methods applied to cosmologies with positive cosmological constant and specific symmetry groups.
result Asymptotically, 3+1D cosmologies evolve to de Sitter space under certain conditions.
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. 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.
Study of cosmic microwave background polarization using spin random fields.
problem Detecting deviations from Gaussianity and anisotropies in cosmic fields.
method Explicit formula for Lipschitz-Killing curvatures of spin spherical random fields.
result Coherent with asymptotic results, providing new metric expressions.
Bayesian Gaussian Processes improve exoplanet transit and Hubble constant inference.
problem Improving exoplanet transit and Hubble constant inference using Bayesian Gaussian Processes.
method Kernel-, mean- and noise-marginalised Gaussian Processes with evidence-based model comparison and transdimensional sampling.
result Inferred Hubble constant H0 values from cosmic chronometers, baryon acoustic oscillations and combined datasets are 66±6kms−1Mpc−1, 67±10kms−1Mpc−1 and 69±6kms−1Mpc−1, respectively. 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.
An immense class of physical counterexamples to the four dimensional strong cosmic censor conjecture---in its usual broad formulation---is exhibited. More precisely, out of any closed and simply connected 4-manifold an open Ricci-flat Lorentzian 4-manifold is constructed which is not globally hyperbolic and no perturba…
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.
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.
In this paper we construct new solutions of the Kahler-Yang-Mills equations, by applying dimensional reduction methods to the product of the complex projective line with a compact Riemann surface. The resulting equations, that we call gravitating vortex equations, describe Abelian vortices on the Riemann surface with b…
Many tasks in computer vision can be cast as a "label changing" problem, where the goal is to make a semantic change to the appearance of an image or some subject in an image in order to alter the class membership. Although successful task-specific methods have been developed for some label changing applications, to da…
TomOpt optimizes muon detector designs using differentiable programming.
problem Designing efficient particle detectors for muon tomography.
method Differentiable programming for muon interaction modeling, inference, and optimisation.
result Demonstrated end-to-end differentiable and inference-aware optimisation of particle physics instruments.
We carry out the harmonic analysis on four Platonic spherical three-manifolds with different topologies. Starting out from the homotopies (Everitt 2004), we convert them into deck operations, acting on the simply connected three-sphere as the cover, and obtain the corresponding variety of deck groups. For each topology…
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 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.