10 problems

Consider the spherically symmetric Einstein--Maxwell charged scalar field (EMCSF) model and an interpolating family of Cauchy data with critical parameter $p_*$, whose critical dev…

Let $D_v$ denote the covariant derivative in the interior null direction $v$, let $\phi$ be the scalar field, and consider solutions of equations … . A quantity is oscillatory towa…

Let a scalar field evolve on a subextreme Kerr black-hole interior, with initial data subject to the relevant perturbation class. The evolution reaches a Cauchy horizon across whic…

Let $\mathcal{Q}^+$ be the quotient spacetime, $\mathcal{I}^+$ future null infinity, and let the black-hole asymptotic charge mean the limiting charge appearing in the model. Nonze…

Let $\mathcal{Q}^+$ be the quotient spacetime, $\mathcal{I}^+$ future null infinity, and interpret “sub-extremal in the limit” as the limiting black-hole condition stated in the pa…

Let $\mathcal{Q}^+$ be the quotient spacetime, $\mathcal{I}^+$ future null infinity, and $\mathcal{S}$ the relevant singular boundary component. Space-like singularity conjecture.…

Let $\mathcal{Q}^+$ be the quotient spacetime, $\mathcal{I}^+$ future null infinity, $\mathcal{S}$ the non-central $r=0$ boundary component, $\mathcal{CH}_{i^+}$ the Cauchy horizon…

Hod–Piran conjecture. Among all admissible, sufficiently regular and decaying data, there exists a generic subclass such that, whenever the maximal future development satisfies…

Let $(\mathcal M,g)$ be extremal Kerr spacetime with mass $M$ and angular momentum per unit mass $a$, where $M=|a|\neq 0$. Let $\phi$ be an axisymmetric solution of … arising from…

Let $(\mathcal M,g)$ be extremal Reissner–Nordström spacetime with mass $M$ and charge $e$, where $M=|e|\neq 0$. Let $\phi$ solve the wave equation … with sufficiently regular Cauc…