New nonuniform black string solutions

TL;DR

The paper numerically constructs static nonuniform vacuum black strings in $D=5$ and $D=6$, analyzes their mass, tension, temperature, and entropy using quasilocal and counterterm formalisms, and introduces a deformation parameter $\lambda$ that tracks horizon waist. It finds qualitative agreement between the $D=5$ and $D=6$ cases, including backbending of the nonuniform-string branch and indications that the nonuniform string and black-hole branches merge at a topology-changing transition at a critical tension $n_*$, consistent with KK phase-diagram expectations. It also shows how to generate Einstein–Maxwell–dilaton black strings from vacuum seeds via a Harrison transformation for arbitrary dilaton coupling $a$, including strings in a Melvin background, while preserving key thermodynamic relations such as the invariant product $TS$ and relating charges to the seed solution. Together, these results strengthen the conjectured merger of branches at a topology-changing transition, reveal a richer phase structure across dimensions, and extend the solution space to charged and magnetized configurations with practical implications for higher-dimensional gravity in KK scenarios.

Abstract

We present nonuniform vacuum black strings in five and six spacetime dimensions. The conserved charges and the action of these solutions are computed by employing a quasilocal formalism. We find qualitative agreement of the physical properties of nonuniform black strings in five and six dimensions. Our results offer further evidence that the black hole and the black string branches merge at a topology changing transition. We generate black string solutions of the Einstein-Maxwell-dilaton theory by using a Harrison transformation. We argue that the basic features of these solutions can be derived from those of the vacuum black string configurations.