On the shape of rotating black-holes

MARÍA EUGENIA GABACH CLEMENT; REIRIS MARTIN

PHYSICAL REVIEW D - PARTICLE AND FILDS

American Physical Society

Año: 2013

0556-2821

We give a thorough description of the shape of rotating axisymmetric stable black-hole(apparent) horizons applicable in dynamical or stationary regimes. It is found that rota-tion manifests in the widening of their central regions (rotational thickening), limits theirglobal shapes to the extent that stable holes of a given area A and angular momentum J=0form a precompact family (rotational stabilization) and enforces their whole geometry tobe close to the extreme-Kerr horizon geometry at almost maximal rotational speed (en-forced shaping). The results, which are based on the stability inequality, depend only onA and J . In particular they are entirely independent of the surrounding geometry of thespace-time and of the presence of matter satisfying the strong energy condition. A com-plete set of relations between A, J , the length L of the meridians and the length R of thegreatest axisymmetric circle, is given. We also provide concrete estimations for the dis-tance between the geometry of horizons and that of the extreme Kerr, in terms only of Aand J . Besides it own interest, the work has applications to the Hoop conjecture as formu-lated by Gibbons in terms of the Birkhoff invariant, to the Bekenstein-Hod entropy boundsand to study the compactness of classes of stationary black-hole space-times.