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28 March 2024
 
  » arxiv » 0912.4001

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The Brown-York mass and the Thorne hoop conjecture
Niall O Murchadha ; Roh-Suan Tung ; Naqing Xie ; Edward Malec ;
Date 20 Dec 2009
AbstractThe 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 $C < 2pi M_{BY}$, 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.
Source arXiv, 0912.4001
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