Einstein-Gauss-Bonnet Black Rings at Large $D$

We study the black ring solution in the Einstein-Gauss-Bonnet (EGB) theory at large $D$. By using the $1/D$ expansion in the near horizon region we derive the effective equations for the slowly rotating black holes in the EGB theory. The effective equations describe the non-linear dynamics of various stationary solutions, including the EGB black ring, the slowly rotating EGB black hole and the slowly boosted EGB black string. By different embeddings we construct these stationary solutions explicitly. By performing the perturbation analysis of the effective equations, we obtain the quasinormal modes of the EGB black ring. We find that thin EGB black ring becomes unstable against non-axisymmetric perturbation.Furthermore, we numerically evolve the effective equations in a particular case to study the final state of the instability, and find that the thin black ring becomes the stable non-uniformblack ring at late time, which gives a relative strong evidence to support the conjecture given in [arXiv:1510.02200].