Shielding gravity fields using special potentials.
problem Gravitational shielding challenges.
method Third-order metric potentials for linearised gravity.
result Avoids solving singular equations in shielding.
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48 results for “gravitational shielding”
New method parameterizes solutions to linearized vacuum constraints on Einstein manifolds.
problem Parameterizing solutions to linearized vacuum constraints on Einstein manifolds.
method Parameterize solutions using unconstrained potentials and shield linearized gravitational fields.
result Showed how to shield linearized gravitational fields without TT gauge for any value of cosmological constant.
We perform an optimal localization of asymptotically flat initial data sets and construct data that have positive ADM mass but are exactly trivial outside a cone of arbitrarily small aperture. The gluing scheme that we develop allows to produce a new class of -body solutions for the Einstein equation, which patently…
Study shows large extra dimensions are hidden from view by black holes.
problem Difficulty in observing large extra dimensions in the universe.
method Analysis of conditions leading to black hole formation in lower dimensional theories.
result Extra dimensions larger than are hidden inside black holes.
Model analyzes debt recycling strategies under various fiscal regimes and jurisdictions.
problem Understanding debt recycling dynamics and their impact on repayment times and equity growth.
method Developed a calibrated model incorporating mortgage interest rates, borrowing costs, and tax shields.
result Introducing positive interest rates without tax shields contracts success regions and lengthens repayment times, but tax shields partially reverse these effects.
Shielded LMC samples from non-convex spaces with repulsive drift.
problem Sampling from non-convex spaces with convex holes.
method Combining adaptive temperature and repulsive drift.
result Advantages over unconstrained sampling in constrained spaces.
Safe reinforcement learning for robots using model predictive shielding.
problem Ensuring safety of learned policies in robotics tasks.
method Model Predictive Shielding (MPS) that switches between learned and backup policies.
result Guaranteed safety of learned policies in challenging robotics tasks.
Evaluates SHIELD's effectiveness against adaptive adversaries in various threat models.
problem Evaluating SHIELD's efficacy against adaptive adversaries in different threat models.
method Empirical analysis of SHIELD's robustness against adaptive attacks using Projected Gradient Descent (PGD) attacks in various threat models (white-box, gray-box).
result The targeted PGD attack success rate drops from 64.3% to 48.9% when models are trained from scratch instead of retrained.
Positive mass theorems for spin initial data sets with arbitrary ends and dominant energy shieldsmath.DG
Proves positive mass theorem for spin initial data sets with arbitrary ends and dominant energy shields.
problem Proving the positive mass theorem for spin initial data sets with various ends and energy shields.
method Modification of Witten's approach involving an additional independent timelike direction in the spinor bundle.
result Positive mass theorem for spin initial data sets with arbitrary ends and dominant energy shields.
Generalizes nonnegativity result for Brown-York mass using noncompact fill-ins.
problem Proving nonnegativity of Brown-York mass for noncompact fill-ins.
method Extending positive mass theorem to noncompact and shielded fill-ins.
result Proves nonnegativity of mean curvature for noncompact NNSC fill-ins.
New proof shows spacetime energy is always positive in higher dimensions.
problem Proving spacetime positive energy in arbitrary dimensions.
method Combines Schoen-Yau, Eichmair, Jang equation, shielding principle.
result Spacetime positive energy theorem proven in arbitrary dimensions.
New method provides scalable safety guarantees for RL agents.
problem Safe reinforcement learning in real-life scenarios.
method State-augmentation and shield design for probabilistic avoidance.
result Strict formal safety guarantees for RL agents, scalable and practical.
Extends positive mass theorem to arbitrary dimensions using a new inductive scheme.
problem Overcoming singularities in the Schoen-Yau proof for arbitrary dimensions.
method Inductive scheme combining shielding principle, conformal blow-up, and Cheeger-Naber bound.
result Proof of positive mass theorem in arbitrary dimensions.
Proves positive mass theorem for hyperbolic manifolds with ends.
problem Establishing positive mass theorem for complex initial data sets.
method Used spectral PSC, Jang equation, and quantitative shielding theorem.
result Proved positive mass theorem for asymptotically hyperbolic manifolds.
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
Classifies ALG and ALH gravitational instantons.
problem Classifying gravitational instantons with specific curvature properties.
method Extending Hein's construction and proving a Torelli-type theorem.
result Shows that Hein's construction is the only ALG gravitational instanton.
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.
Improves diversity of text-to-image models without sacrificing FID.
problem Lack of diversity and tendency to recreate training set images.
method Adds sparse repellency terms to diffusion SDE to guide trajectories away from a reference set.
result Improves diversity of diffusion models with minimal impact on FID.
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.
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
Study of gravitational radiation using quasi-local energy.
problem Gravitational radiation and its measurement.
method Evaluation of Wang-Yau quasi-local mass on Schwarzschild spacetime.
result Quantification of gravitational radiation through quasi-local energy.
Defense strategy improves controller robustness against adversarial attacks.
problem Adversarial attacks on learning-enabled controllers in CPS.
method Two-stage defense strategy treating controller and environment as black-boxes with unknown dynamics.
result Defense strategy effectively improves controller robustness in realistic control domains.
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.
Generalizes gravitational instanton metrics to a new class.
problem Finding explicit expressions for gravitational instantons.
method Quaternionic-based Ansatz generalizing Gibbons-Hawking Ansatz.
result Explicit expressions for type gravitational instantons.
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 gravitational energy measure $\Q$ found in higher dimensions.
problem Characterizing local gravitational energy in higher dimensions.
method Study of quasilocal mass proposals in higher dimensions.
result New quantity $\Q$ replaces Bel-Robinson superenergy in vacuum limits.
TensorShield defends images from adversarial attacks using tensor decomposition.
problem Adversarial attacks on images can fool deep neural networks.
method Tensor decomposition to find low-rank approximations of images, reducing high-frequency perturbations.
result TensorShield outperforms existing methods like SLQ by 14% against FGSM attacks.
Constructs solutions for gravitational instantons from minimal surfaces.
problem Finding solutions for gravitational instantons.
method Using correspondence between minimal surfaces and gravitational instantons, derived explicit maximal surface solutions.
result Explicit solutions for maximal surface with zero mean curvature.
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.
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…
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.
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.
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 …
Geometrically constructs energy-tensors for gauge and gravitational fields.
problem Defining natural energy-tensors for gauge and gravitational fields.
method Prolongation of connections to connections of bundles, using the jet space formulation.
result Natural geometric object for joint energy-tensors of matter and gauge fields.
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 …