language: en

April 24, 2008

[16:2 WSPC/142-IJMPD 01219]

[International Journal of Modern Physics D Vol. 17, Nos. 3 & 4 (2008) 519?523]

[c World Scientific Publishing Company]

THE INEQUALITY BETWEEN MASS AND ANGULAR MOMENTUM FOR AXIALLY SYMMETRIC BLACK HOLES *

SERGIO DAIN
Facultad de Matemática, Astronoma y Fsica,
Universidad Nacional de Córdoba, Ciudad Universitaria, (5000) Córdoba, Argentina
Max Planck Institute for Gravitational Physics, (Albert Einstein Institute),
Am Mühlenberg 1, D-14476 Potsdam, Germany
dain@famaf.unc.edu.ar Received 01 December 2007

[Communicated by D. V. Ahluwalia-Khalilova]

In this essay I first discuss the physical relevance of the inequality m ? p |J| for axially symmetric (nonstationary) black holes, where m is the mass and J the angular momentum of the space?time. 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 about the physical implications of this characterization for the nonlinear stability problem for black holes.

Keywords: Black holes; axial symmetry; angular momentum; mass; extreme Kerr.

1. Introduction