Explosive black hole fission and fusion in large extra dimensions

TL;DR

The paper analyzes the phase structure of black objects in $\mathbb{R}^{3+1} \times \mathbf{S}^1$ with a large extra dimension, introducing the dimensionless parameter $\mu=(G_5 M)/L^2$ and comparing horizon topologies to predict a first-order, hysteretic transition between black-string and black-hole phases. It leverages a phase-diagram framework featuring the Gregory-Laflamme instability at $\mu_{GL}$ and topology-change near merger to delineate stable regions and transition pathways, including the fission ($\text{string} \rightarrow \text{BH}$) and fusion ($\text{BH} \rightarrow \text{string}$) channels. Energetics are quantified by $\Delta M=\eta M$ with $M\simeq L/G_4$, a timescale $\tau\sim L$, and a power scale $P\sim \eta/G_4$, yielding Planck-like bursts whose energy scales with the size of the extra dimension $L$. The results suggest observable signatures of large extra dimensions in both astrophysical phenomena and high-energy experiments, while highlighting key numerical unknowns ($\eta_{1,2}$, $\mu_1$, $\mu_2$) that determine the precise transition dynamics.

Abstract

Black holes are the densest form of energy, and in the presence of compact dimensions black objects may take one of several forms including the black-hole and the black-string, the simplest relevant background being R^{3+1} * S^1. Recent understanding of the first order nature of the transition indicate a powerful ``hysteresis'' curve, where black objects may undergo fusion or fission during a tachyonic decay with Planck power and duration of the order of the size of the compact dimension L. Such explosions which scale with L could be test signatures for large extra dimensions in either astronomical observations or accelerators.