Brown-York mass and the thorne hoop conjecture

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Ó Murchadha, Niall
Tung, Roh-Suan
Xie, Naqing
Malec, Edward
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The Thorne hoop conjecture is an attempt to make precise the notion that gravitational collapse occurs if enough energy is compressed into a small enough volume, with the "size" being defined by the circumference. We can make a precise statement of this form, in spherical symmetry, using the Brown-York mass as our measure of the energy. Consider a spherical 2-surface in a spherically symmetric spacetime. If the Brown-York mass M(BY) and the circumference C satisfy C<2 pi M(BY), then the system must either have emerged from a white hole or will collapse into a black hole. We show that no equivalent result can hold true using either the Liu-Yau mass M(LY) or the Wang-Yau mass M(WY). This forms a major obstacle to any attempt to establish a Thorne-type hoop theorem in the general case based on either the Liu-Yau or the Wang-Yau mass.
Quasi local energy , Trapped surfaces , general relativity , Vacuum spacetimes , Black hole , Matter
Ó Murchadha, N., Tung, R.-S., Xie, N. and Malec, E. (2010) 'Brown-York mass and the thorne hoop conjecture', Physical Review Letters, 104(4), 041101 (4pp). doi: 10.1103/PhysRevLett.104.041101
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