Black rings at large D

TL;DR

This paper develops an effective theory for slowly rotating black holes in the large D limit, deriving solutions including black rings and analyzing their stability and quasinormal modes.

Contribution

It introduces an analytic framework for black rings at large D, providing solutions and stability analysis that extend previous numerical approaches.

Findings

Black rings are analytically constructed at large D.

Thin black rings are unstable against non-axisymmetric perturbations.

1/D corrections influence the stability and properties of black rings.

Abstract

We study the effective theory of slowly rotating black holes at the infinite limit of the spacetime dimension D. This large D effective theory is obtained by integrating the Einstein equation with respect to the radial direction. The effective theory gives equations for non-linear dynamical deformations of the slowly rotating black hole as effective equations. The effective equations contain the slowly rotating Myers-Perry black hole, slowly boosted black string, non-uniform black string and black ring as stationary solutions. We obtain an analytic solution of the black ring by solving the effective equations. Furthermore, by perturbation analysis of the effective equations, we find a quasinormal mode condition of the black ring in analytic way. As a result we confirm that thin black ring is unstable against non-axisymmetric perturbations. We also include 1/D corrections to the effective equations and discuss the effects by 1/D corrections.