Lower Bounds for the Area of Black Holes in Terms of Mass, Charge, and Angular Momentum

Abstract

The most general formulation of Penrose's inequality yields a lower bound for ADM mass in terms of the area, charge, and angular momentum of black holes. This inequality is in turn equivalent to an upper and lower bound for the area in terms of the remaining quantities. In this note, we establish the lower bound for a single black hole in the setting of axisymmetric maximal initial data sets for the Einstein-Maxwell equations, when the non-electromagnetic matter fields are not charged and satisfy the dominant energy condition. It is shown that the inequality is saturated if and only if the initial data arise from the extreme Kerr-Newman spacetime. Further refinements are given when either charge or angular momentum vanish. Lastly, we discuss the validity of the lower bound in the presence of multiple black holes.

12 pages; section 2 revised; to appear in Phys. Rev. D

References in corpus (3)

• Mass and angular-momentum inequalities for axi-symmetric initial data sets. II. Angular-momentum
• Mass and angular-momentum inequalities for axi-symmetric initial data sets I. Positivity of mass
• On the Riemannian Penrose inequality with charge and the cosmic censorship conjecture

Cited by in corpus (14)

• Proof of the Riemannian Penrose Inequality with Charge for Multiple Black Holes
• Geometric inequalities for black holes
• Extensions of the Charged Riemannian Penrose Inequality
• Reduction Arguments for Geometric Inequalities Associated With Asymptotically Hyperboloidal Slices
• Deformations of Charged Axially Symmetric Initial Data and the Mass-Angular Momentum-Charge Inequality
• Mass angular momentum and charge inequalities for black holes in Einstein-Maxwell-axion-dilaton gravity
• Relating Mass to Angular Momentum and Charge in 5-Dimensional Minimal Supergravity
• Notes on several phenomenological laws of quantum gravity
• Bounding Horizon Area by Angular Momentum, Charge, and Cosmological Constant in 5-Dimensional Minimal Supergravity
• The Positive Mass Theorem with Angular Momentum and Charge for Manifolds with Boundary
• Penrose inequalities and a positive mass theorem for charged black holes in higher dimension
• Remarks on mass and angular momenta for $U(1{)}^2$-invariant initial data
• The Penrose inequality in spherical symmetry with charge and in Gauss-Bonnet gravity
• Area inequalities for stable marginally outer trapped surfaces in Einstein-Maxwell-dilaton theory