Einstein-Gauss-Bonnet black strings at large $\alpha$

The simplest black string in higher-dimensional general relativity (GR) is perhaps the direct product of a Schwarzschild spacetime and a flat spatial direction. However, it is known that the Einstein-Gauss-Bonnet theory does not allow such a trivial and simple solution. We propose a novel analytic technique, which assumes that the Gauss-Bonnet (GB) term becomes dominant over the Einstein-Hilbert (EH) term. Assuming the dimensionless coupling constant $\alpha$ normalized by the horizon scale is large enough, we find that the spacetime is separated into the GB region and GR region, which are matched via the transition region where the GB and EH terms are comparable. Using this large $\alpha$ approximation, we indeed construct new analytic solutions of black strings, from which we analytically compute various physical quantities of black strings at large $\alpha$. Moreover, we confirm that all these analytic results are consistent with the numerical calculation. We also discuss the possible extension to general Einstein-Lovelock black holes.