# Phases and Stability of Non-Uniform Black Strings

## TL;DR

This paper constructs and analyzes non-uniform black string solutions across a wide range of dimensions, revealing their thermodynamic and dynamic stability properties and confirming the existence of a critical dimension where stability characteristics change.

## Contribution

It extends the large-D perturbative approach to include higher-order corrections, providing detailed insights into the stability and thermodynamics of non-uniform black strings across dimensions.

## Key findings

- Confirmed the existence of Sorkin's critical dimension with high precision.
- Demonstrated the change in thermodynamic and dynamic stability at the critical dimension.
- Mapped the parameter space for non-uniform black strings in various dimensions.

## Abstract

We construct solutions of non-uniform black strings in dimensions from $D \approx 9$ all the way up to $D = \infty$, and investigate their thermodynamics and dynamical stability. Our approach employs the large-$D$ perturbative expansion beyond the leading order, including corrections up to $1/D^4$. Combining both analytical techniques and relatively simple numerical solution of ODEs, we map out the ranges of parameters in which non-uniform black strings exist in each dimension and compute their thermodynamics and quasinormal modes with accuracy. We establish with very good precision the existence of Sorkin's critical dimension and we prove that not only the thermodynamic stability, but also the dynamic stability of the solutions changes at it.