Study limits of quasi-local angular momentum at infinity of gravitating systems.
problem Understanding limits of quasi-local angular momentum at infinity of gravitating systems.
method Based on optimal isometric embedding and quasilocal mass theory, the study defines and analyzes the limits of quasi-local angular momentum at spatial and null infinity.
result Limits of quasi-local angular momentum are discussed at spatial and null infinity of an isolated gravitating system.
Researchers find non-abelian symmetric gravitating vortices on a sphere.
problem Finding solutions to non-abelian gravitating vortex equations on a sphere.
method Dimensional reduction of Kähler-Yang-Mills-Higgs equations, reduction to ODEs, method of continuity.
result Existence and admissible volumes of solutions proved.
Unified approach to constructing integrable systems using Stäckel lifts.
problem Constructing new integrable Hamiltonian systems.
method Generalized Stäckel geometry and Haantjes structure.
result Hamiltonian systems with momentum-dependent Stäckel matrices exhibit symplectic-Haantjes structures.
Study shows how electromagnetic and gravitational waves can form trapped surfaces.
problem Formation of trapped surfaces from initial data with electromagnetic fields.
method Established a scale-critical semi-global existence result from past null infinity for the Einstein-Maxwell system.
result Generalized approach for studying Einstein vacuum equations and extended a result to scale-critical regime.
In a previous paper on coupled gravitational and electromagnetic perturbations of Reissner-Nordström spacetime in a polarized setting, we derived a system of wave equations for two independent quantities, one related to the Weyl curvature and one related to the Ricci curvature of the perturbed spacetime. We analyze her…
Study of twistor spaces and minitwistor spaces for ALE gravitational instantons.
problem Characterizing the geometry of ALE gravitational instantons of type Amodd. method Analyzing the base locus of linear systems and using distinguished twistor lines.
result Explicit determination of images of certain twistor lines and description of real minitwistor lines.
Study finds periodic orbits in a complex gravitational system.
problem Existence of periodic solutions in a gravitational system with multiple primaries.
method Proves existence of periodic solutions when primaries move on a Hip-Hop solution.
result Proves the existence of periodic solutions in the restricted (2N+1)-body problem. New magnetic memory effects found in gravitational waves and memory.
problem Understanding new effects in gravitational waves and memory.
method Analyzing asymptotically-flat spacetimes with slow decay.
result Diverging magnetic memory sourced by curvature and neutrino cloud.
Existence and uniqueness of gravitating vortices on Riemann surfaces with specific properties.
problem Existence and uniqueness of gravitating vortices on compact Riemann surfaces.
method Existence via solving a continuity path, proving existence of singular gravitating vortices, and establishing existence of singular Einstein-Bogomol'nyi equations.
result Existence and uniqueness of gravitating vortices on Riemann surfaces with suitable properties.
The paper proves extremal black holes form at a critical point of gravitational collapse.
problem Formation of extremal black holes in gravitational collapse.
method Constructing smooth families of spherically symmetric solutions to the Einstein-Maxwell-Vlasov system.
result Extremal Reissner-Nordström black holes form at the critical collapse threshold.
New proof of Schwarzschild stability using geometric gauge.
problem Linear stability of Schwarzschild spacetime under gravitational perturbations.
method Employing a new geometric gauge and exploiting the structure of transport equations.
result Established both orbital and asymptotic stability for linearised quantities.
Neural networks improve gravitational-wave parameter estimation.
problem Estimating parameters of binary black hole systems from gravitational-wave data.
method Autoregressive normalizing flows for likelihood-free inference.
result Performance comparable to current best deep-learning approaches, with fast sampling.
Study global solutions for Boussinesq systems on curved manifolds.
problem Global existence and uniqueness of solutions to Boussinesq systems on non-compact Riemannian manifolds with gravitational fields.
method Used dispersive and smoothing estimates of a vectorial matrix semigroup to establish global existence and uniqueness of mild solutions for linear systems. Then, applied fixed point arguments to semilinear systems. Proved exponential stability using Gronwall's inequality.
result Established global existence, uniqueness, and exponential stability of mild solutions to the Boussinesq systems on non-compact Riemannian manifolds with gravitational fields.
Constructs initial data for Einstein vacuum equations involving multiple localized gravitational sources.
problem Modeling the interaction of distant gravitational systems in general relativity.
method Time-symmetric initial data construction using gluing schemes and localized sources.
result Produces initial data sets with finite ADM mass and multiple Einstein-Rosen bridges.
We derive a system of equations governing the coupled gravitational and electromagnetic perturbations of Reissner-Nordström spacetime. The equations are derived in the context of global non-linear stability of Reissner-Nordström under axially symmetric polarized perturbations, as a generalization of the recent work on …
New estimates quantify blow-up rates of spacelike singularities in gravitational collapse.
problem Quantifying the blow-up rates of spacelike singularities in gravitational collapse.
method Deriving new quantitative estimates using spherical symmetry and double-null coordinates.
result Polynomial blow-up rates O(1/rN) for various quantities, with improved estimates for r∂ur and r∂vr. New framework for gravitational perturbations of Kerr spacetimes, focusing on stability.
problem Stability of Kerr spacetimes to gravitational perturbations.
method New geometric framework with tailored null frames and gauge, reformulating Einstein equations.
result Derivation of linearised vacuum Einstein equations in the new framework.
The study finds polynomial upper bounds for singularities in Einstein-scalar field system.
problem Understanding the strength of singularities in gravitational collapse.
method Analyzing geometric quantities, focusing on the Kretschmann scalar.
result Polynomial blow-up upper bounds O(1/rN) for the Kretschmann scalar, improving previous bounds. In the last few years, machine learning techniques, in particular convolutional neural networks, have been investigated as a method to replace or complement traditional matched filtering techniques that are used to detect the gravitational-wave signature of merging black holes. However, to date, these methods have not …
Paper proves trapped surface formation for EMCSF system without symmetry assumptions.
problem Formation of trapped surfaces for the Einstein--Maxwell--charged scalar field system.
method Scale-critical trapped surface formation result established from past null infinity.
result Focusing of gravitational waves, concentration of electromagnetic fields, or condensation of scalar fields can lead to trapped surface formation.
Researchers resolved ambiguities in gravitational radiation charges.
problem Ambiguities in charges related to gravitational radiation.
method Addressed supertranslation ambiguities in classical and extended BMS algebras.
result Proposed and proved an invariant charge free from supertranslation ambiguity.
Classifies gravitational instantons with quadratic volume growth.
problem Classifying gravitational instantons with specific growth properties.
method Proves a classification theorem for ALG∗ gravitational instantons, determines topology, and proves existence of uniform coordinates. result Proves a relationship between ALG gravitational instantons of different orders.
Survey of recent progress in gravitational instantons
problem Classification of hyperkähler and Hermitian gravitational instantons
method Survey of recent progress in gravitational instantons
result Survey of recent progress in gravitational instantons
We prove boundedness and polynomial decay statements for solutions to the spin ±2 generalized Teukolsky system on a Reissner-Nordström background with small charge. The first equation of the system is the generalization of the standard Teukolsky equation in Schwarzschild for the extreme component of the curvature $…
The paper proves unique characterization of gravitational instantons with specific volume growth.
problem Characterizing gravitational instantons with quadratic volume growth.
method Defining a period mapping and proving its surjectivity and openness.
result The periods uniquely characterize ALG∗ and ALG gravitational instantons up to diffeomorphism. Period maps surjective for certain gravitational instantons.
problem Understanding the uniformization of gravitational instantons.
method Uniformization theorems by Chen--Chen, Chen--Viaclovsky, Collins--Jacob--Lin, and Hein--Sun--Viaclovsky--Zhang.
result Period maps surjective for ALH*, ALG, and ALG* gravitational instantons.
Authors prove Torelli theorem for a specific type of gravitational instantons.
problem Identifying diffeomorphism types of gravitational instantons.
method Using mirror special Lagrangian fibrations and recent work on rational elliptic surfaces.
result Identify 10 diffeomorphism types of ALHb∗ gravitational instantons. 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 Cloc0,1-inextendibility of certain spacetimes. When a spacetime takes Bondi radiating metric, and is vacuum and asymptotically flat at spatial infinity which ensures the positive mass theorem, we prove that the standard ADM energy-momentum is the past limit of the Bondi energy-momentum. We also derive a formula relating the ADM energy-momentum of any asymptotically…
The paper proves a rigidity theorem for null geodesic travel times in asymptotically AdS spacetimes.
problem Determining if a spacetime is conformally AdS based on null geodesic travel times.
method Analyzing all null geodesics from a point to its antipodal point, considering various spacetime conditions.
result The spacetime is conformally AdS if and only if all null geodesics from a point refocus at its antipodal point.
This is our third paper in a series on the gravitational instantons. In this paper, we classify ALG and ALH gravitational instantons. In ALG case, we extend Hein's construction slightly and show that it's the only ALG gravitational instanton. In ALH case, we prove a Torelli-type theorem.
Gravitational instantons are non-Kähler, providing a counterexample to Euclidean Black Hole Uniqueness.
problem Classical Euclidean Black Hole Uniqueness conjecture
method Analyzing the Chen-Teo gravitational instanton
result The Chen-Teo instanton is Hermitian and non-Kähler
Deep learning speeds up gravitational wave analysis.
problem Computational challenge in analyzing gravitational wave data.
method Trained a neural-network to model posterior probability distributions over 15-dimensional system parameters.
result Generated accurate posterior samples at high speed.
This article aims to present an elementary analytical solution to the question of the formation of a structure of differentiation of rates of return in a classical gravitation model and in a model of the dynamics of price-wage spirals.
New solutions of gravity from branes wrapped on orbifolds.
problem Constructing new AdS2×M4 solutions in gauged supergravity.
method Uplifting to massive type IIA, wrapping D4-D8 branes on orbifolds, using gravitational blocks.
result Entropy of solutions matches extremizing an entropy function.
Existence proved for specific types of gravitational instantons.
problem Existence of toric ALE and ALF gravitational instantons.
method Established existence and uniqueness results for ALE and ALF gravitational instantons.
result Existence of a unique, Ricci-flat, toric ALE and ALF gravitational instanton for every admissible rod structure.
This is our second paper in a series to study gravitational instantons, i.e. complete hyperkäler 4-manifolds with faster than quadratic curvature decay. We prove two main theorems: 1.The asymptotic rate of gravitational instantons to the standard models can be improved automatically. 2.Any ALF-D_k gravitational instant…
New method for efficient inference over complex parameter spaces.
problem Challenges in Bayesian inference for high-dimensional, intractable likelihoods.
method Arbitrary Marginal Neural Ratio Estimation (AMNRE) for simulation-based inference.
result Efficient inference over arbitrary subsets of parameters without numerical integration.
Study on instability of extreme Reissner-Nordström spacetime perturbations.
problem Linear stability of gravitational and electromagnetic perturbations in extreme Reissner-Nordström spacetime.
method Extends Giorgi's framework to prove instability results for a set of gauge invariant quantities along the event horizon.
result Proves decay, non-decay, and polynomial blow-up estimates for certain quantities along the event horizon, depending on the number of derivatives.
Proves infinitesimal rigidity of Hermitian gravitational instantons.
problem Understanding the moduli space of Hermitian gravitational instantons.
method Proof of infinitesimal rigidity and integrability using boundary conditions and conformal Kähler properties.
result Completes the understanding of Hermitian gravitational instantons, both compact and non-compact.
The holographic description in the presence of gravitational Chern-Simons term is studied. The modified gravitational equations are integrated by using the Fefferman-Graham expansion and the holographic stress-energy tensor is identified. The stress-energy tensor has both conformal anomaly and gravitational or, if re-f…
Second paper in series solves Einstein vacuum equations for three impulsive waves.
problem Solving local Cauchy problem for impulsive gravitational waves.
method Geometric commutators for energy estimates, fractional-derivative regularity, anisotropic Sobolev embedding.
result Scalar field becomes everywhere Lipschitz and C1,θ away from singular region. Study proves interaction of three impulsive gravitational waves, showing local solution and Lipschitz continuity.
problem Interaction of three impulsive gravitational waves in Einstein vacuum equations.
method Geometric estimates and wave estimates to prove local solution and continuity.
result Local solution to Einstein vacuum equations with three impulsive gravitational waves, Lipschitz continuity.
Ehlers-Kundt conjecture is a physical assertion about the fundamental role of plane waves for the description of gravitational waves. Mathematically, it becomes equivalent to a problem on the Euclidean plane R2 with a very simple formulation in Classical Mechanics: given a non-necessarily autonomous potent…
New approach proves existence of gravitating vortices on Riemann surfaces.
problem Existence of gravitating vortices on Riemann surfaces.
method Symplectic reduction by stages and reduced α-K-energy. result Existence of solutions implies polystability of effective divisors.
Review of gravitational instantons in physics.
problem Understanding solutions to Einstein equations in four dimensions.
method Lecture review of examples.
result Examples of gravitational instantons.
Gravitational instantons collapse to a punctured plane with a special Kahler metric.
problem The collapse of gravitational instantons from a complex structure limit.
method Analysis of a sequence of ALH*-gravitational instantons and their collapse to a punctured plane.
result The moduli space of pointed ALH*-gravitational instantons collapses to a punctured plane with a special Kahler metric.
The holographic duality can be extended to include quantum theories with broken coordinate invariance leading to the appearance of the gravitational anomalies. On the gravity side one adds the gravitational Chern-Simons term to the bulk action which gauge invariance is only up to the boundary terms. We analyze in detai…