We show how to reduce the general formulation of the mass-angular momentum-charge inequality, for axisymmetric initial data of the Einstein-Maxwell equations, to the known maximal case whenever a geometrically motivated system of equations admits a solution. It is also shown that the same reduction argument applies to …
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48 results for “mass-angular momentum-charge inequality”
Proves mass-angular momentum-charge inequality in 5D minimal supergravity.
problem Mass-angular momentum-charge inequality in 5D minimal supergravity.
method Proved inequality for a broad class of initial data.
result Charged Myers-Perry black holes are unique minimizers.
Establishes inequalities linking body size, mass, angular momentum, and charge.
problem Understanding the relationship between a body's size, mass, angular momentum, and charge.
method Analyzes axisymmetric initial data sets for the Einstein equations, using a computable notion of size.
result Provides black hole existence criteria even in the time-symmetric case.
In this paper, we extend the work in \cite{D}\cite{ChrusLiWe}\cite{ChrusCo}\cite{Co}. We weaken the asymptotic conditions on the second fundamental form, and we also give an norm bound for the difference between general data and Extreme Kerr data or Extreme Kerr-Newman data by proving convexity of the renormali…
Transformations of Asymptotically AdS Hyperbolic Initial Data and Associated Geometric Inequalitiesgr-qc
Transforms hyperbolic to flat data, deriving geometric inequalities.
problem Deriving geometric inequalities in asymptotically AdS hyperbolic spacetimes.
method Constructs transformations preserving physical quantities to relate hyperbolic to flat spacetimes.
result Derives geometric inequalities from flat counterparts.
In this paper a lower bound for the ADM mass is given in terms of the angular momenta and charges of black holes present in axisymmetric initial data sets for the Einstein-Maxwell equations. This generalizes the mass-angular momentum-charge inequality obtained by Chrusciel and Costa to the case of multiple black holes.…
The Area-Angular Momentum-Charge Inequality for Black Holes With Positive Cosmological Constantgr-qc
Researchers prove a black hole inequality involving area, angular momentum, and charge.
problem Establishing a new inequality for black holes with a positive cosmological constant.
method Reduced to minimizing an area functional related to a harmonic map energy, maps from 2-sphere to complex hyperbolic plane.
result The inequality is saturated for extreme Kerr-Newman-de Sitter horizons.
Mass inequality for black ring spacetimes, showing extreme solutions.
problem Establishing mass-angular momentum relation for black ring spacetimes.
method Mathematical derivation of mass-angular momentum inequality.
result The inequality is saturated for extreme Pomeransky-Sen'kov black ring solutions.
The study finds the minimum mass for bi-axisymmetric black holes with spherical topology.
problem Finding the minimum mass for bi-axisymmetric black holes.
method Analyzing extreme Myers-Perry initial data for 5-dimensional spacetimes.
result Proves the mass-angular momentum inequality for bi-axisymmetric black holes.
Establishes a Penrose-type inequality for axisymmetric initial data with angular momentum and charge.
problem Establishing a Penrose-type inequality for axisymmetric initial data with angular momentum and charge.
method Maximal, axisymmetric initial data for the Einstein-Maxwell equations satisfying the weak energy condition. Rigidity statement proven.
result Reduces to the conjectured Penrose inequality with angular momentum and charge under certain conditions.
Study finds area inequalities for black hole horizons in 5D minimal supergravity.
problem Bounding the area of black hole horizons in 5D minimal supergravity.
method Established area-angular momentum-charge inequalities for stable marginally outer trapped surfaces with symmetry.
result Unique geometries saturating the inequalities correspond to extreme black hole solutions.
In this paper, we proved the mass angular momentum inequality\cite{D1}\cite{ChrusLiWe}\cite{SZ} for axisymmetric, asymptotically flat, vacuum constraint data sets with small trace. Given an initial data set with small trace, we construct a boost evolution spacetime of the Einstein vacuum equations as \cite{ChOM}. Then …
We show how to reduce the general formulation of the mass-angular momentum inequality, for axisymmetric initial data of the Einstein equations, to the known maximal case whenever a geometrically motivated system of equations admits a solution. This procedure is based on a certain deformation of the initial data which p…
The paper extends mass and angular momentum theorems for specific symmetrical initial data.
problem Extending mass and angular momentum theorems to -invariant initial data.
method Using Brill's positive mass theorem and extending a local mass angular momenta inequality result.
result The extension of mass and angular momentum theorems to a broader class of initial data sets.
The abstract discusses geometric inequalities related to black hole formation.
problem Establishing geometric inequalities for black hole formation.
method Applying Bekenstein's entropy bounds and Penrose's inequality to axisymmetric bodies.
result New criteria for black hole formation involving angular momentum, charge, and matter energy.
Establishes inequality for multiple black holes, proving mass lower bound.
problem Proving mass-angular momentum inequality for multiple black holes.
method Novel flow of singular harmonic maps with hyperbolic plane target.
result Mass lower bound for ADM mass and angular momentum.
Study of harmonic maps with extreme Kerr-like singularities.
problem Analyzing harmonic maps with specific singularities.
method Asymptotic analysis of harmonic maps from 3D Euclidean space to hyperbolic plane.
result Existence and classification of tangent harmonic maps at extreme black hole horizons.
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.
This paper studies the canonical Chow quotient of a smooth projective variety by a reductive algebraic group. The main purpose is to give some topological interpretations and characterization of Chow quotient which have the advantage to be more intuitive and geometric. This is to be done over the field of complex numbe…
New definitions of center of mass and angular momentum in general relativity.
problem Difficulties in defining energy, momentum, and center of mass in general relativity.
method First principles in general relativity and geometric analysis.
result Consistency of classical formula p=mv with Einstein's field equation.
Formulae for mass and angular momentum transformations under BMS transformations derived from curvature and metric.
problem Deriving transformation formulae for mass and angular momentum under BMS transformations.
method Two approaches: from curvature tensor and metric coefficients.
result Exact expressions for Drey-Streubel angular momentum of a general section.
This work removes logarithmic singularities from hyperboloidal initial data without creating new ones.
problem Logarithmic singularities in hyperboloidal initial data sets.
method Evolutionary framework of the constraint equations and generalization of Beyer and Ritchie's result.
result Generic solutions of the constraint equations are free of logarithmic singularities.
This paper proves a canonical foliation on null infinity for Kerr-like black holes.
problem Establishing well-defined physical quantities on null infinity for Kerr-like black holes.
method Existence and uniqueness results for GCM spheres by Klainerman-Szeftel.
result Existence of a canonical foliation on future null infinity with well-defined physical quantities.
The isoperimetric inequalitymath.DG
The isoperimetric inequality and related inequalities are explored.
problem Proving the isoperimetric inequality and related inequalities.
method Discussing classical and recent proofs.
result Various proofs of the isoperimetric inequality and Sobolev inequality.
New proof of Willmore inequality using geometric divergence inequality.
problem Proving the Willmore inequality for bounded domains.
method Using a parametric geometric inequality derived from a divergence form geometric differential inequality.
result New proofs of quantitative Willmore-type and weighted Minkowski inequalities.
Lorentz-Finsler geometry reveals new and old inequalities.
problem Finding new inequalities using Lorentz-Finsler geometry.
method Applying reverse Cauchy-Schwarz and reverse triangle inequalities in Lorentz-Finsler geometry.
result Proved new and refined inequalities, including refinements of Aczél's inequality.
The paper derives new inequalities on manifolds and applies them to convex hypersurfaces.
problem Deriving new inequalities on manifolds and convex hypersurfaces.
method Using Fourier theory and geometric implications of Poincare-type inequalities.
result Sharp Minkowski-type inequalities, including stability and Alexandrov-Fenchel inequalities.
The paper proves inequalities on Finsler manifolds under Ricci curvature bounds.
problem Proving -Sobolev and Nash inequalities on Finsler metric measure manifolds.
method Global -Poincaré inequality, -Sobolev inequality, Nash inequality derivation.
result Established global optimal -Sobolev inequality with a sharp constant.
New inequality on sphere generalizes circle inequality.
problem Generalizing circle inequality to sphere.
method Develops a new inequality on the sphere that incorporates mass center deviation.
result Improves Aubin's inequality and Onofri's inequality.
Paper proves anisotropic Minkowski inequality and related inequalities.
problem Proving anisotropic Minkowski inequality and related inequalities.
method Utilizes a nonlinear potential theoretic approach.
result Sharp anisotropic Minkowski inequality and related inequalities proved.
Explains geometric inequalities for minimal hypersurfaces.
problem Geometric inequalities for minimal hypersurfaces.
method Expository discussion of known inequalities.
result Discussion of classical inequalities for minimal hypersurfaces.
The paper finds new inequalities for convex polygons.
problem Finding precise inequalities for convex polygons.
method Analytic isoperimetric inequalities based on Schur convex functions, followed by Bonnesen-style and inverse Bonnesen-style inequalities.
result Sharp discrete isoperimetric inequalities for planar convex polygons.
Study shows household inequality accounts for 30% of total global income inequality.
problem Intra-household inequality is often overlooked in studies of income inequality.
method Used LIS micro data to analyze inequality trends in 1973-2013 across multiple countries.
result At least 30% of total global income inequality is due to intra-household inequality.
The study improves Bochner inequality on Finsler manifolds to derive important inequalities.
problem Improving Bochner inequality on Finsler manifolds to derive new inequalities.
method Using improved Bochner inequality and its integrated form, the study derives a sharp Poincaré-Lichnerowicz inequality, a new proof for logarithmic Sobolev inequality, and an estimate of geodesic ball volumes.
result Derivation of new inequalities and estimates on Finsler manifolds.
Paper provides an example showing CD inequality doesn't imply CDE' inequality.
problem Relationship between CD inequality and CDE' inequality.
method Provides a counterexample.
result CD inequality does not imply CDE' inequality.
The paper proves various inequalities on gradient shrinking Ricci solitons.
problem Understanding geometric inequalities on gradient shrinking Ricci solitons.
method Proving multiple inequalities equivalent on complete gradient shrinking Ricci solitons.
result Various inequalities (Sobolev, logarithmic Sobolev, Schrödinger, etc.) are equivalent on gradient shrinking Ricci solitons.
Sharp inequalities for star bodies in 2D space.
problem Understanding star bodies in 2D space.
method Sharp inequalities for star bodies in .
result New inequalities and proofs for star bodies.
Sharp inequality found on three-balls for fourth order Sobolev traces.
problem Fourth order Sobolev trace inequality on three-balls.
method Established through equivalence to a third order Sobolev inequality on two-spheres.
result Sharp fourth order Sobolev trace inequality on three-balls.
The paper develops inequalities for log-concave functions and related surface areas.
problem Understanding log-concave functions and their inequalities.
method Establishing new inequalities through f-divergences and functional affine surface areas.
result New inequalities on functional affine surface area and bounds for Kullback-Leibler divergence.
Sharp inequalities derived from fractional Sobolev inequalities on spheres.
problem Deriving sharp inequalities from fractional Sobolev inequalities.
method Alternative elementary argument using fractional Sobolev inequalities.
result Sharp Moser-Trudinger-Onofri inequalities derived from fractional Sobolev inequalities.
The paper extends matrix inequalities to various types of matrices.
problem Generalizing inequalities for different types of matrices.
method Extending known inequalities for real, complex, and quaternionic matrices.
result New inequalities for matrices in subspaces spanned by Clifford systems or algebras.
Study on functional inequalities on simple edge spaces.
problem Whether classical functional inequalities hold in simple edge spaces.
method Analyzing Sobolev and Poincaré inequalities, proving optimality of Sobolev constant.
result Optimality result concerning the B-constant of the Sobolev inequality.
Proves inequalities on curved spaces with positive curvature.
problem Proving inequalities on manifolds with nonnegative Ricci curvature.
method Analyzes manifolds with nonnegative Ricci curvature and Euclidean volume growth.
result Proves Heisenberg-Pauli-Weyl, Hardy-Sobolev, and Caffarelli-Kohn-Nirenberg inequalities.
The paper derives inequalities on Finsler manifolds, influenced by their curvatures.
problem Deriving inequalities on Finsler manifolds.
method Local and global geometric inequalities on Riemannian and Finsler manifolds.
result Generalized Caffarelli-Kohn-Nirenberg and Hardy type inequalities on Finsler manifolds.
Paper refines Talagrand inequality on Euclidean spaces.
problem Improving Talagrand inequality for Euclidean spaces.
method Symmetrization and alternative proof methods.
result Several refined functional inequalities derived.
New inequalities for convex curves with multiple geometric factors.
problem Establishing inequalities for convex curves with multiple geometric factors.
method Parametric isoperimetric-type inequalities for closed convex curves with parameter conditions and equality conditions.
result Derived new inequalities and improved versions of existing inequalities.
Alternative proofs for various inequalities on Riemannian manifolds.
problem Various functional inequalities on Riemannian manifolds.
method Generic functional inequality, Riccati pairs, solving Riccati-type ODE.
result Alternative proofs for multiple inequalities, including Hardy-type and Caccioppoli inequalities.
Study on Riemannian isoperimetric inequality, finding it true generically.
problem Direct analogue of Euclidean isoperimetric inequality is false on Riemannian manifolds.
method Used Lojasiewicz-Simon inequality for real analytic metrics.
result Modified quantitative isoperimetric inequality holds for real analytic metrics.