10 problems

Let $(\gamma,k)$ be the initial data from Theorem, with ADM mass $\mathfrak m_0$ and vanishing linear momentum, let $g$ be the resulting spacetime metric, and set…

Let $M$ be the mass, $J$ the angular momentum, and $M_2$ the mass quadrupole of an axisymmetric black hole. Multipole bound conjecture. The quadrupole should satisfy … The bound is…

Consider the merger of two nonspinning black holes, and let an extremal Kerr black hole mean a rotating black hole whose dimensionless spin approaches its maximal allowed value. Sp…

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…

Vacuum Schwarzschild-to-Kerr characteristic gluing conjecture. The Schwarzschild symmetry sphere of mass $M_i$ and radius $R_i$ can be characteristically glued to any such non-anti…

The Einstein vacuum equations describe a Lorentzian metric $g$ on a $3+1$-dimensional manifold $\mathcal{M}$ by … where $\Lambda$ is the cosmological constant. A Kerr black hole is…

Let $\Sigma_0$ be a complete $2$-ended asymptotically flat Cauchy hypersurface in a Kerr spacetime with $0<|a|<M$, and let $\psi$ solve the linear wave equation … The relevant assu…

Let $\Sigma_0$ be a Cauchy hypersurface in a subextremal rotating Kerr spacetime, and let $\psi$ solve the linear wave equation … Assume the initial data on $\Sigma_0$ are smooth a…

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…

Asymptotic stability of the Kerr family. The maximal Cauchy development of a small perturbation of sub-extremal Kerr initial data possesses a black hole and exterior region, and in…