Mass and angular-momentum inequalities for axi-symmetric initial data sets I. Positivity of mass

Abstract

We extend the validity of Brill's axisymmetric positive energy theorem to all asymptotically flat initial data sets with positive scalar curvature on simply connected manifolds.

33 pages in A4

References in corpus (6)

• Progress in relativistic gravitational theory using the inverse scattering method
• Mass and angular-momentum inequalities for axi-symmetric initial data sets. II. Angular-momentum
• Killing vectors in asymptotically flat space-times: I. Asymptotically translational Killing vectors and the rigid positive energy theorem
• The Positive Mass and Isoperimetric Inequalities for Axisymmetric Black Holes in four and five dimensions
• Proof of the (local) angular momemtum-mass inequality for axisymmetric black holes
• The isometry groups of asymptotically flat, asymptotically empty space-times with timelike ADM four-momentum

Cited by in corpus (36)

• Stationary Black Holes: Uniqueness and Beyond
• Mass and angular-momentum inequalities for axi-symmetric initial data sets. II. Angular-momentum
• Black hole Area-Angular momentum inequality in non-vacuum spacetimes
• Mass and Angular Momentum in General Relativity
• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
• Geometric inequalities for axially symmetric black holes
• Angular momentum-mass inequality for axisymmetric black holes
• Mass, angular-momentum, and charge inequalities for axisymmetric initial data
• A Dain Inequality with charge
• Lower Bounds for the Area of Black Holes in Terms of Mass, Charge, and Angular Momentum
• Axisymmetric evolution of Einstein equations and mass conservation
• Geometrical inequalities bounding angular momentum and charges in General Relativity
• Extreme throat initial data set and horizon area--angular momentum inequality for axisymmetric black holes
• A uniqueness theorem for degenerate Kerr-Newman black holes
• Existence of singularities in two-Kerr black holes
• Geometric inequalities for black holes
• Convexity of reduced energy and mass angular momentum inequalities
• Specifying angular momentum and center of mass for vacuum initial data sets
• Horizon area--angular momentum inequality for a class of axially symmetric black holes
• Bekenstein Bounds, Penrose Inequalities, and Black Hole Formation
• Bounds on the force between black holes
• On the classification of stationary electro-vacuum black holes
• Reduction Arguments for Geometric Inequalities Associated With Asymptotically Hyperboloidal Slices
• Inequalities Between Size, Mass, Angular Momentum, and Charge for Axisymmetric Bodies and the Formation of Trapped Surfaces
• Mass angular momentum and charge inequalities for black holes in Einstein-Maxwell-axion-dilaton gravity
• Recent progress on the positive energy theorem
• Mass angular momentum inequality for axisymmetric vacuum data with small trace
• Mathematical general relativity: a sampler
• On 3+1 Lorentzian Einstein Manifolds with One Rotational Isometry
• A lower bound for the mass of axisymmetric connected black hole data sets
• Axially symmetric spacetimes: numerical and analytical perspectives
• The Positive Mass Theorem with Angular Momentum and Charge for Manifolds with Boundary
• Remarks on mass and angular momenta for $U(1{)}^2$-invariant initial data
• Stability of the Positive Mass Theorem for Axisymmetric Manifolds
• Angular momentum-mass inequality for axisymmetric black holes
• On extreme Kerr-throats and zero temperature black-holes