7 problems

Binary black hole (BBH) merger waveforms are gravitational-wave signals produced during the coalescence of two black holes; integrability means that the underlying dynamical system…

Let the initial data be for the Einstein–Maxwell equations, and let their maximal Cauchy development be the corresponding spacetime solution. Consider a suitable finite-codimension…

Define the bounded-motion region … where $R$ is the Kerr radial potential, $r^*$ is the local maximum of $-R$, and $r_*$ is the local minimum of $-R$ to its right. Generic Kerr bou…

Let $N_\varepsilon$ be the perturbed normally hyperbolic invariant manifold associated with the Kerr photon shell, and let $(a,M,E,Q,L_z)$ satisfy the conditions in assumption (2)…

Define the bounded-motion region … Here $E$ is the particle energy, $L$ its angular momentum, $V$ the effective potential, and $H$ the Hamiltonian. Generic Schwarzschild bounded-ph…

Let $N_\varepsilon$ denote the perturbed normally hyperbolic invariant manifold associated with the photon sphere, and let $L$ and $L_z$ be the angular-momentum quantities used in…

Consider vacuum spacetimes arising from generic asymptotically flat Cauchy data with one end, not necessarily initially close to Kerr. Generic settling conjecture. Such spacetimes…