On the fate of black string instabilities: An Observation

TL;DR

This paper discusses the fate of black string instabilities, analyzing whether they lead to breakup into black holes or are prevented by geometric bounds, with implications for understanding singularity formation.

Contribution

It provides an argument that black string pinch-off at finite advanced time is a natural outcome consistent with previous bounds on horizon behavior.

Findings

Pinch-off at finite advanced time is plausible under derived bounds.

Infinite affine parameter may correspond to finite advanced time in horizon evolution.

The results support the possibility of black string breakup into black holes.

Abstract

Gregory and Laflamme (hep-th/9301052) have argued that an instability causes the Schwarzschild black string to break up into disjoint black holes. On the other hand, Horowitz and Maeda (arXiv:hep-th/0105111) derived bounds on the rate at which the smallest sphere can pinch off, showing that, if it happens at all, such a pinch-off can occur only at infinite affine parameter along the horizon. An interesting point is that, if a singularity forms, such an infinite affine parameter may correspond to a finite advanced time -- which is in fact a more appropriate notion of time at infinity. We argue below that pinch-off at a finite advanced time is in fact a natural expectation under the bounds derived by Horowitz and Maeda.