Evolution of a black hole-inhabited brane close to reconnection

Abstract: Last moments of a mini black hole escaping from a brane are studied. It is argued that at the point of reconnection, where the piece of the brane attached to the black hole separates from the rest, the worldsheet of the brane becomes isotropic (light-like). The degenerate mode of evolution, with the worldsheet isotropic everywhere, is investigated. In particular, it is shown that the brane approaches the reconnection point from below if it reconnects within a certain limit distance, and from above if it reconnects beyond that distance. The rate of relaxation to the degenerate mode is established. If the dimension of the brane is $p$, the nondegeneracy, measured by the determinant of the relevant part of the induced metric tensor, falls down as (latitudinal angle)$^{2(p - 1)}$.