Schwarzschild uniqueness conjecture for non-flat AF0 gravitational instantons

Let $(M,g)$ be a non-flat $\operatorname{AF}_0$ gravitational instanton. Schwarzschild uniqueness conjecture. The metric $g$ is, up to isometry, the Schwarzschild metric. Evidence is available under an isometric semi-free $S^1$-action compatible with the $\operatorname{AF}_0$ asymptotics, but the general assertion is open.