The Hoop Conjecture in Spherically Symmetric Spacetimes

Details The Hoop Conjecture in Spherically Symmetric Spacetimes The Hoop Conjecture in Spherically Symmetric Spacetimes

2009-12-17

arxiv.org/abs/0912.3533v1

Phys.Rev.D80:124025,2009

Mathematics

Differential Geometry

Scientific paper

10.1103/PhysRevD.80.124025

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.

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