Dynamics and Stability of Black Rings

TL;DR

This paper investigates the stability and dynamics of neutral black rings, revealing that thin rings are generally stable against radial perturbations but may face Gregory-Laflamme instabilities, with some stable parameter ranges identified.

Contribution

It provides a detailed analysis of the forces and instabilities in black rings, including radial and Gregory-Laflamme instabilities, and explores their thermodynamic properties.

Findings

Fat black rings are radially unstable.

Thin black rings are radially stable but may have Gregory-Laflamme instabilities.

Most neutral black rings are classically unstable, with some stable parameter ranges.

Abstract

We examine the dynamics of neutral black rings, and identify and analyze a selection of possible instabilities. We find the dominating forces of very thin black rings to be a Newtonian competition between a string-like tension and a centrifugal force. We study in detail the radial balance of forces in black rings, and find evidence that all fat black rings are unstable to radial perturbations, while thin black rings are radially stable. Most thin black rings, if not all of them, also likely suffer from Gregory-Laflamme instabilities. We also study simple models for stability against emission/absorption of massless particles. Our results point to the conclusion that most neutral black rings suffer from classical dynamical instabilities, but there may still exist a small range of parameters where thin black rings are stable. We also discuss the absence of regular real Euclidean sections of black rings, and thermodynamics in the grand-canonical ensemble.