The Brown-York mass and the Thorne hoop conjecture

Details The Brown-York mass and the Thorne hoop conjecture The Brown-York mass and the Thorne hoop conjecture

2009-12-20

arxiv.org/abs/0912.4001v1

Phys.Rev.Lett.104:041101,2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

4 pages; accepted for publication in Physical Review Letters

Scientific paper

10.1103/PhysRevLett.104.041101

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.

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