Black hole black string phase transition in Einstein-Gauss-Bonnet gravity

We investigate the presence of a black hole string phase transition in Einstein Gauss Bonnet (EGB) gravity large dimension limit. The merger point is static spacetime connecting with phase. consider several ranges Gauss-Bonnet parameter. find that there range when corrections are subordinate to terms limit, and yet geometry does not approach away from neck. cannot rule out topology changing as argued by Kol. However asymptotically it obvious directly also demonstrate for another parameter, approaches certain parameter depending on $\alpha$ parameters Einstein-Gauss-Bonnet metric small enough.