New proof of instability for certain Einstein metrics.
problem Einstein metrics on specific 4-manifolds.
method Proving instability of conformally Kähler, Einstein metrics.
result Proven instability of certain Einstein metrics.
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48 results for “gravitational instability”
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.
A robust proof of the instability of naked singularities of a scalar field in spherical symmetrygr-qc
Published in 1999, Christodoulou proved that the naked singularities of a self-gravitating scalar field are not stable in spherical symmetry and therefore the cosmic censorship conjecture is true in this context. The original proof is by contradiction and sharp estimates are obtained strictly depending on spherical sym…
Proves stability of gravitational instantons, proving operator positivity.
problem Stability of gravitational instantons.
method Riemannian analog of black hole mode stability for Hermitian, non-self-dual gravitational instantons.
result Teukolsky equation is a positive definite operator on Hermitian, non-self-dual gravitational instantons.
Study shows instability of naked singularities in perfect fluid models.
problem Instability of naked singularities in Einstein equations coupled with isothermal perfect fluid.
method Investigated spherically symmetric self-similar naked singularities under perturbations of an external massless scalar field.
result Spherically symmetric self-similar naked singularities are unstable to trapped surface formation.
Study examines the training process of an unsupervised learning model for detecting gravitational-wave transient noise.
problem Transient noise in gravitational-wave detector data causes instability and signal overlap.
method Unsupervised deep learning with variational autoencoder and invariant information clustering applied to the Gravity Spy dataset.
result Training process of the unsupervised learning architecture is examined and reported.
TIER uses extended strain data to improve gravitational wave detection sensitivity.
problem Improving gravitational wave detection sensitivity using extended strain data.
method TIER framework using machine learning to capture extended strain data features.
result Up to 20% improvement in sensitive volume time in LIGO-Virgo-Kagra O3 data.
Instability of spherical naked singularities of a scalar field under gravitational perturbationsgr-qc
In this paper, we initiate the study of the instability of naked singularities without symmetries. In a series of papers, Christodoulou proved that naked singularities are not stable in the context of the spherically symmetric Einstein equations coupled with a massless scalar field. We study in this paper the next simp…
Unsupervised learning classifies transient noise in gravitational wave detectors.
problem Transient noise interferes with gravitational wave signals, causing instability.
method Combines variational autoencoder and invariant information clustering.
result Consistent classification with Gravity Spy project labels.
Riemannian geometrical tools, such as Ricci collineations and Killing symmetries, so often used in Einstein general theory of gravitation are here applied to plasma physics to build magnetic surfaces from Einstein plasma metrics used in tokamak devices. It is shown that the Killing symmetries are constrains the Einstei…
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.
We argue that the Einstein gravity theory can be reformulated in almost Kahler (nonsymmetric) variables with effective symplectic form and compatible linear connection uniquely defined by a (pseudo) Riemannian metric. A class of nonsymmetric theories of gravitation (NGT) on manifolds enabled with nonholonomic distribut…
The inequality relating total mass and angular momenta, is established for (possibly dynamical) spacetimes admitting black holes of ring () topology. This inequality is shown to be sharp in the sense that it is saturated precisely…
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
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 gravitational instantons.
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
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…
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…
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.
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.
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 -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…
Researchers embed gravitational instantons in higher-dimensional spaces.
problem Embedding gravitational instantons in higher-dimensional spaces.
method Construct isometric and conformally isometric embeddings of gravitational instantons in and .
result Embedding class of the Einstein--Maxwell instanton is equal to 3.
Gravitational waves are predicted by the general theory of relativity. In [6] D. Christodoulou showed that gravitational waves have a nonlinear memory. We proved in [3] that the electromagnetic field contributes at highest order to the nonlinear memory effect of gravitational waves. In the present paper, we study this …
Charge measurements for instantons and gravitational perturbations.
problem Evaluating charges in Hermitian non-Kähler Einstein 4-manifolds and their perturbations.
method Evaluation of charges via Killing spinors and perturbation analysis of gravitational instantons.
result Generic gravitational perturbations admit a closed 2-form measuring the charge change.
In this paper we explicitly calculate the analogue of the 't Hooft SU(2) Yang--Mills instantons on Gibbons--Hawking multi-centered gravitational instantons which come in two parallel families: the multi-Eguchi--Hanson, or A_k ALE gravitational instantons and the multi-Taub--NUT, or A_k ALF gravitational instantons. We …
In general relativity, the local gravitational energy is best characterised by the quasilocal mass. The small sphere limit of quasilocal mass provides us the most local notion of gravitational energy. In four dimensions, the limits were shown be the stress tensor in non-vacuum and the Bel-Robinson tensor in vacuum. We …
Study of twistor spaces and minitwistor spaces for ALE gravitational instantons.
problem Characterizing the geometry of ALE gravitational instantons of type .
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 on mode stability of gravitational instantons of type D.
problem Proving mode stability of gravitational instantons of type D.
method Analogous to Lorentzian case, analyze Weyl curvature scalars satisfying a separable Teukolsky equation.
result Prove mode stability, showing no solutions compatible with regularity and asymptotic flatness.
Elliptic analysis on collapsing gravitational instantons modelled using the Gibbons-Hawking ansatzmath.DG
The paper studies gravitational instantons with flat limits and finds elliptic regularity estimates.
problem Analyzing gravitational instantons with flat limits using elliptic analysis.
method Establishing elliptic regularity estimates and showing uniform constants for a family of metrics.
result The Laplacian is Fredholm and an isomorphism between specific weighted spaces.
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 construct explicit bundles for ALF metrics, revealing rational patching matrices for gravitational instantons.
problem Constructing explicit toric Ricci-flat metrics and their associated bundles.
method Explicit construction of patching matrices for ALF metrics and gravitational instantons.
result Rational form of patching matrices for gravitational instantons in the Chen--Teo family.
This paper is the sequel of our previous article "From ALE to ALF gravitational instantons", where we constructed ALF hyperkahler metrics on minimal resolutions of dihedral Kleinian singularities. In the present article we generalize the construction to smooth deformations of these Kleinian singularities, with help of …
Construction of gravitational instantons with non-maximal volume growth via codimension-1 collapsemath.DG
The paper constructs gravitational instantons with unique collapse patterns.
problem Creating gravitational instantons with specific geometric properties.
method Using gluing construction, the metric collapses to quotients of R^3 with specific patterns.
result The constructed gravitational instantons have unique collapse patterns and exceptional points.
We improve current instability-based methods for the selection of the number of clusters in cluster analysis by developing a normalized cluster instability measure that corrects for the distribution of cluster sizes, a previously unaccounted driver of cluster instability. We show that our normalized instability mea…
Gravitational wave memory increases faster than Brownian motion in early universe and astrophysical sources.
problem Detecting gravitational wave memory from early universe and astrophysical sources.
method Investigated gravitational wave sources in early universe and astrophysical settings, showing memory increases faster than Brownian motion.
result Gravitational wave memory increases following a power law, faster than the scaling law of Brownian motion.
Researchers solve field equations for special gravitational instantons.
problem Solving field equations for conformally Kähler Riemannian four-manifolds.
method Developed a framework to solve the field equations for generalised gravitational instantons using conformal self-duality and cosmological Einstein-Maxwell.
result Found conformally self-dual and Einstein-Maxwell generalisations of specific geometries.
Study toric gravitational instantons using rod structures and inequalities.
problem Classify toric ALE/ALF instantons.
method Express signature in terms of rod structure, apply Hitchin-Thorpe inequalities, analyze rod structures with three turning points.
result Necessary conditions for rod structures of toric ALE/ALF instantons.
Simulation-based inference speeds up gravitational wave data analysis.
problem High-dimensional parameter spaces and complex noise in gravitational wave data.
method Simulation-based inference methods using machine learning techniques.
result Simulation-based inference methods improve speed over traditional methods.
Solves time-optimal navigation on slippery slopes with cross gravitational wind.
problem Time-optimal navigation on a slippery cross slope under gravitational wind.
method New Finsler metric derived for the problem, considering both lateral and longitudinal gravitational effects.
result Conditions for strong convexity and purely geometric solution provided.
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.