4 problems

Lapedes' conjecture. The only non-trivial AF gravitational instantons with a 2-torus isometry are the Euclidean Kerr manifolds.

Cosmological-horizon instability conjecture. Every horizon of cosmological type is necessarily unstable. In particular, every static solution to problem has at most one horizon of…

Uniqueness of the Kerr family. Any sufficiently regular, asymptotically flat, and stationary solution to $\operatorname{Ric}(g)=0$ which is bounded by a non-degenerate event horizo…

Let $(\mathbb{T}{M},g)$ be a spin spacetime that is asymptotically flat or Kaluza–Klein, whose Ricci tensor satisfies the null-convergence condition, and that admits an action of…