The area-angular momentum inequality for black holes in cosmological spacetimes

Autor(en)

Maria Eugenia Gabach Clement, Martin Reiris, Walter Simon

Abstrakt

For a stable, marginally outer trapped surface (MOTS) in an axially symmetric spacetime with cosmological constant λ > 0 and with matter satisfying the dominant energy condition, we prove that the area A and the angular momentum J satisfy the inequality 8π|J| ≤ A√(1 - λA/4π)(1 - λA/12π), which is saturated precisely for the extreme Kerr-de Sitter family of metrics. This result entails a universal upper bound |J| ≤ J

_max ≈ 0.17/λ for such MOTS, which is saturated for one particular extreme configuration. Our result sharpens the inequality 8π |J| ≤ A (Dain and Reiris 2011 Phys. Rev. Lett. 107 051101, Jaramillo, Reiris and Dain 2011 Phys. Rev. Lett. D 84 121503), and we follow the overall strategy of its proof in the sense that we first estimate the area from below in terms of the energy corresponding to a 'mass functional', which is basically a suitably regularized harmonic map S

² → H

². However, in the cosmological case this mass functional acquires an additional potential term which itself depends on the area. To estimate the corresponding energy in terms of the angular momentum and the cosmological constant we use a subtle scaling argument, a generalized 'Carter-identity', and various techniques from variational calculus, including the mountain pass theorem.

Organisation(en)

Gravitationsphysik

Externe Organisation(en)

Gottfried Wilhelm Leibniz Universität Hannover, Universidad Nacional de Córdoba

Journal

Classical and Quantum Gravity

Band

32

Anzahl der Seiten

23

ISSN

0264-9381

DOI

https://doi.org/10.1088/0264-9381/32/14/145006

Publikationsdatum

07-2015

Peer-reviewed

Ja

ÖFOS 2012

103036 Theoretische Physik, 103004 Astrophysik

Schlagwörter

ASJC Scopus Sachgebiete

Physics and Astronomy (miscellaneous)

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/3e6948d8-8f54-48da-b0b4-8b82056203fb