The Hoop Conjecture in Spherically Symmetric Spacetimes

Abstract

We give general sufficient conditions for the existence of trapped surfaces due to concentration of matter in spherically symmetric initial data sets satisfying the dominant energy condition. These results are novel in that they apply and are meaningful for arbitrary spacelike slices, that is they do not require any auxiliary assumptions such as maximality, time-symmetry, or special extrinsic foliations, and most importantly they can easily be generalized to the nonspherical case once an existence theory for a modified version of the Jang equation is developed. Moreover, our methods also yield positivity and monotonicity properties of the Misner-Sharp energy.

References in corpus (1)

• The Jang equation, apparent horizons, and the Penrose inequality

Cited by in corpus (16)

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• On the shape of bodies in General Relativistic regimes
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• Bekenstein Bounds, Penrose Inequalities, and Black Hole Formation
• Analytical studies on the hoop conjecture in charged curved spacetimes
• Inequalities Between Size and Charge for Bodies and the Existence of Black Holes Due to Concentration of Charge
• Inequalities Between Size, Mass, Angular Momentum, and Charge for Axisymmetric Bodies and the Formation of Trapped Surfaces
• The inequality between size and charge in spherical symmetry
• Investigations on hoop conjecture for horizonless spherical charged stars
• Cosmic Cloaking of Rich Extra Dimensions
• Testing generalized spacetimes for black holes using the Hod function representation of the hoop conjecture
• A unified hoop conjecture for black holes and horizonless compact stars
• Shape of black holes
• Existence of Black Holes Due to Concentration of Angular Momentum