A Soliton and a Black Hole are in Gauss-Bonnet gravity. Who wins?

We study here the phase-transitional evolution between the Eguchi-Hanson soliton, the orbifolded Schwarzschild Anti de-Sitter black hole, and orbifolded thermal Anti de-Sitter space in Gauss-Bonnet gravity for a small Gauss-Bonnet coefficient $\alpha$. Novel phase structure is uncovered for both negative and positive $\alpha$ with spacetime configurations that are stable in Gauss-Bonnet gravity without being so in Einsteinian gravity. The evolutionary tracks taken towards such stable configurations are guided by quantum tunnelling and can be represented with a phase diagram constructed by comparing the Euclidean actions of each of our states as a function of $\alpha$ and the black hole radius $r_b$. According to the AdS/CFT correspondence dictionary, it is expected that some generalized version of closed-string tachyon condensation will exhibit the phase behaviour found here.