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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 | Abstract: | 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 $C < 2pi M_{BY}$, 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 | Services: | Forum | Review | PDF | Favorites |
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