10 problems

Kerr stability conjecture. The maximal Cauchy development of any initial data set for the Einstein vacuum equations, sufficiently close to a subextremal Kerr initial data set in a…

Stability of Kerr–AdS for analytic perturbations. There exists $\rho_0>0$ such that, for every such $(M,a)$ and every sufficiently small $\epsilon>0$, there is…

Let ${\bf g}_{M,a}$ be a subextremal Kerr metric. Let $(\Sigma_0,g_0,k_0)$ be a suitably small perturbation of its initial data, where $\Sigma_0$ is a 3-dimensional manifold, $g_0$…

An extremal Kerr black hole is a Kerr black hole with parameters satisfying $|a|=m$. Despite horizon linear instabilities, codimension-one nonlinear stability conjecture for extrem…

Kerr stability conjecture. The subextremal Kerr exterior family $\big(\mathcal{M},g_{M,a}\big)$ is stable as a family of solutions to the Einstein vacuum equations.

Let $g$ be a Lorentzian metric and $F$ a $2$-form satisfying the Einstein–Maxwell equations … … The final state conjecture in general relativity states that the Kerr–Newman spaceti…

Schwarzschild Cauchy data are Cauchy data induced by a Schwarzschild spacetime. An axially symmetric deformation preserves axial symmetry, and a maximal development is the maximal…

For Kerr--de Sitter parameters $a$, $\Lambda$, and $M$ satisfying … and lying in the shaded region specified by the source, quasinormal modes are complex frequencies $\lambda$ for…

Near-extremal instability conjecture. There exists a neighborhood of the black hole parameters near extremality for which the corresponding regular, non-extremal black holes are li…

The spacetime under consideration satisfies the hypotheses of Theorem … is weakly ultimately Schwarzschildean to order $k+2$. This conjecture is motivated by techniques that obtain…