The inequality between mass and angular momentum for axially symmetric black holes

Abstract

In this essay I first discuss the physical relevance of the inequality $m\ge \sqrt{|J|}$ for axially symmetric (non-stationary) black holes, where m is the mass and J the angular momentum of the spacetime. Then, I present a proof of this inequality for the case of one spinning black hole. The proof involves a remarkable characterization of the extreme Kerr black hole as an absolute minimum of the total mass. Finally, I conjecture on the physical implications of this characterization for the non linear stability problem for black holes.

8 pages, Honorable Mention in the Gravity Research Foundation Essay Competition 2007

References in corpus (4)

• Angular momentum-mass inequality for axisymmetric black holes
• 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
• A variational principle for stationary, axisymmetric solutions of Einstein's equations

Cited by in corpus (17)

• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
• Geometric inequalities for axially symmetric black holes
• Mass, angular-momentum, and charge inequalities for axisymmetric initial data
• A Dain Inequality with charge
• Axisymmetric evolution of Einstein equations and mass conservation
• Extreme throat initial data set and horizon area--angular momentum inequality for axisymmetric black holes
• Geometric inequalities for black holes
• Numerical evidences for the angular momentum-mass inequality for multiple axially symmetric black holes
• Extreme Bowen-York initial data
• Total angular momentum from Dirac eigenspinors
• On well-posedness, linear perturbations and mass conservation for axisymmetric Einstein equation
• Small deformations of extreme Kerr black hole initial data
• On a mass functional for initial data in 4+1 dimensional spacetime
• Linear perturbations for the vacuum axisymmetric Einstein equations
• Avenues for Analytic exploration in Axisymmetric Spacetimes. Foundations and the Triad Formalism
• Axially symmetric spacetimes: numerical and analytical perspectives
• Angular momentum-mass inequality for axisymmetric black holes