title: Brown-york mass and the Thorne hoop conjecture.
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<2piM{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.
authors.affiliation: Center for Astrophysics, Shanghai Normal University, Shanghai, China. niall@ucc.ie
authors.forename: Niall O
authors.initials: NO
authors.lastname: Murchadha
authors.forename: Roh-Suan
authors.initials: RS
authors.lastname: Tung
authors.forename: Naqing
authors.initials: N
authors.lastname: Xie
authors.forename: Edward
authors.initials: E
authors.lastname: Malec