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On non-uniform black branes

Steven S. Gubser

TL;DR

This work analyzes the non-uniform endpoints of the Gregory-Laflamme instability for uncharged black strings in five dimensions using a perturbative expansion around the uniform solution. It constructs static non-uniform branches and computes their thermodynamic properties, finding that the leading-order change in the critical parameter $\eta$ is positive ($\eta_1 \approx 1.45$) while the higher-order entropy difference is negative ($\sigma_2 \approx -0.59$), signaling a first-order transition. The results imply that non-uniform endpoints exist at finite non-uniformity and that the transition from uniform to non-uniform branes is not smooth, with broader implications for other brane systems and their phase structure. The study also discusses methodological challenges, numerical refinements, and future directions for higher-order perturbative analyses and real-time dynamics.

Abstract

Certain black branes are unstable toward fluctuations that lead to non-uniform mass distributions. We study static, non-uniform solutions that differ only perturbatively from uniform ones. For uncharged black strings in five dimensions, we find evidence of a first order transition from uniform to non-uniform solutions.

On non-uniform black branes

TL;DR

This work analyzes the non-uniform endpoints of the Gregory-Laflamme instability for uncharged black strings in five dimensions using a perturbative expansion around the uniform solution. It constructs static non-uniform branches and computes their thermodynamic properties, finding that the leading-order change in the critical parameter is positive () while the higher-order entropy difference is negative (), signaling a first-order transition. The results imply that non-uniform endpoints exist at finite non-uniformity and that the transition from uniform to non-uniform branes is not smooth, with broader implications for other brane systems and their phase structure. The study also discusses methodological challenges, numerical refinements, and future directions for higher-order perturbative analyses and real-time dynamics.

Abstract

Certain black branes are unstable toward fluctuations that lead to non-uniform mass distributions. We study static, non-uniform solutions that differ only perturbatively from uniform ones. For uncharged black strings in five dimensions, we find evidence of a first order transition from uniform to non-uniform solutions.

Paper Structure

This paper contains 12 sections, 36 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Order parameters
  3. Numerics on the black string
  4. Generalities
  5. Solution to $O(\lambda)$
  6. Mass, entropy, and temperature
  7. The zero modes at $O(\lambda^2)$
  8. Higher orders in perturbation theory
  9. Improving and extending the numerics
  10. Interpreting the numerics
  11. Other black branes
  12. Conclusions

Figures (1)

  • Figure 1: (a) Possible curves, drawn schematically in the $\eta$-$\lambda$ plane, describing stationary, uncharged, non-uniform black strings in five dimensions. The solid curve is the likeliest. (b) $\sigma$ versus $\lambda$ for these non-uniform strings. Again, the solid curve is the likeliest.