Highly Deformed Non-uniform Black Strings in Six Dimensions

TL;DR

This paper numerically constructs highly deformed non-uniform black string solutions in six dimensions, revealing a maximum mass and a spiral phase diagram, advancing understanding of black string stability and structure.

Contribution

It introduces an improved pseudo-spectral numerical method to achieve highly deformed black string solutions in six dimensions, uncovering new features in their phase diagram.

Findings

Maximum in the mass curve of black strings

Discovery of a spiral structure in the phase diagram

Identification of additional turning points in the mass

Abstract

We construct numerically static non-uniform black string solutions in six dimensions by using pseudo-spectral methods. An appropriately designed adaptation of the methods in regard of the specific behaviour of the field quantities in the vicinity of our numerical boundaries provides us with extremely accurate results, that allows us to get solutions with an unprecedented deformation of the black string horizon. Consequently, we are able to investigate in detail a critical regime within a suitable parameter diagram. In particular, we observe a clearly pronounced maximum in the mass curve, which is in accordance with the results of Kleihaus, Kunz and Radu from 2006. Interestingly, by looking at extremely distorted black strings, we find two further turning points of the mass, resulting in a spiral curve in the black string's phase diagram.