Evolution of a black hole-inhabited brane close to reconnection

TL;DR

This paper analyzes the final stages of a mini black hole escaping from a brane, focusing on the isotropic worldsheet behavior at reconnection and how the brane approaches this point depending on the reconnection distance.

Contribution

It introduces a detailed study of the degenerate, light-like worldsheet mode during brane reconnection near a black hole, including the rate of relaxation and dependence on brane dimension.

Findings

Brane worldsheet becomes isotropic at reconnection.

The approach to the reconnection point depends on the reconnecting distance.

The nondegeneracy measure decreases as a power law related to brane dimension.

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)$^{2(p - 1)}$.