Brown-York Mass and the Thorne Hoop Conjecture

摘要

The Thorne hoop conjecture is an attempt to make precise the notion that gravitational collapse occursnif enough energy is compressed into a small enough volume, with the ‘‘size’’ being defined by thencircumference. We can make a precise statement of this form, in spherical symmetry, using the Brown-nYork mass as our measure of the energy. Consider a spherical 2-surface in a spherically symmetricnspacetime. If the Brown-York mass MBY and the circumference C satisfy C< 2u0001MBY, then the systemnmust either have emerged from a white hole or will collapse into a black hole. We show that no equivalentnresult can hold true using either the Liu-Yau mass MLY or the Wang-Yau mass MWY. This forms a majornobstacle to any attempt to establish a Thorne-type hoop theorem in the general case based on either thenLiu-Yau or the Wang-Yau mass.