On the shape of rotating black-holes

Abstract

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 rotation manifests in the widening of their central regions (rotational thickening), limits their global shapes to the extent that stable holes of a given area A and angular momentum J (non zero) form a precompact family (rotational stabilization) and enforces their whole geometry to be close to the extreme-Kerr horizon geometry at almost maximal rotational speed (enforced shaping). The results, which are based on the stability inequality, depend only on A and J. In particular they are entirely independent of the surrounding geometry of the space-time and of the presence of matter satisfying the strong energy condition. A complete set of relations between A, J, the length L of the meridians and the length R of the greatest axisymmetric circle, is given. We also provide concrete estimations for the distance between the geometry of horizons and that of the extreme Kerr, in terms only of A and J. Besides it own interest, the work has applications to the Hoop conjecture as formulated by Gibbons in terms of the Birkhoff invariant, to the Bekenstein-Hod entropy bounds and to study the compactness of classes of stationary black-hole space-times.

Changes made to match published version in Phy. Rev. D

References in corpus (3)

• The area of horizons and the trapped region
• Global embedding of the Kerr black hole event horizon into hyperbolic 3-space
• Proof of the area-angular momentum-charge inequality for axisymmetric black holes

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• Late-time cosmological evolution of a general class of f(R, T) gravity with minimal curvature-matter coupling
• Geometric inequalities for black holes
• On the shape of bodies in General Relativistic regimes
• Penrose-like inequality with angular momentum for minimal surfaces
• Size, angular momentum and mass for objects
• Comments on Penrose inequality with angular momentum for outermost apparent horizons
• The inequality between size and charge in spherical symmetry