4 problems

Generic decay conjecture. The generic local-in-space decay rate should be $u^{-6}$ for the curvature components and $r^{2}u^{-6}$ for the metric components.

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…

In grazing collisions of two black holes, let $p$ parameterize initial data, let $p_*$ be the threshold of immediate merger, and let $n$ be the number of orbital revolutions before…

Let $u$ be retarded time along future null infinity $\mathcal I^+$, and let $\Psi^{[4]}$ denote the relevant Newman--Penrose component of a linearised gravitational perturbation. A…