Lower bounds for the area of black holes in terms of mass, charge, and angular momentum

Sergio Dain, Marcus Khuri, Gilbert Weinstein, and Sumio Yamada
Phys. Rev. D 88, 024048 – Published 26 July 2013

Abstract

The most general formulation of Penrose’s inequality yields a lower bound for Arnowitt-Deser-Misner 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 paper, 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. Last, we discuss the validity of the lower bound in the presence of multiple black holes.

  • Received 25 June 2013

DOI:https://doi.org/10.1103/PhysRevD.88.024048

© 2013 American Physical Society

Authors & Affiliations

Sergio Dain1,*, Marcus Khuri2,†, Gilbert Weinstein3,‡, and Sumio Yamada4,§

  • 1Facultad de Matemática, Astronomía y Física, FaMAF, Universidad Nacional de Córdoba, Instituto de Física Enrique Gaviola, IFEG, CONICET, Ciudad Universitaria, 5000 Córdoba, Argentina
  • 2Department of Mathematics, Stony Brook University, Stony Brook, New York 11794, USA
  • 3Department of Physics; Department of Computer Science and Mathematics, Ariel University of Samaria, Ariel 40700, Israel
  • 4Department of Mathematics, Gakushuin University, Tokyo 171-8588, Japan

  • *dain@famaf.unc.edu.ar
  • khuri@math.sunysb.edu
  • gilbert.weinstein@gmail.com
  • §yamada@math.gakushuin.ac.jp

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Issue

Vol. 88, Iss. 2 — 15 July 2013

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