Brown-York mass and the hoop conjecture in nonspherical massive systems

We discuss the relation between the concentration of the Brown-York mass and the formation of trapped surfaces in nonspherical massive systems. In particular, we formulate and prove a precise version of the Thorne hoop conjecture in conformally flat three-geometries sliced by equipotential foliation leaves. An intriguing relationship between the total rest mass and the Brown-York mass is shown. This is a further investigation of the previous work on the Brown-York mass hoop conjecture in spherical symmetry.