7 problems

Generic transverse blow-up conjecture. For generic data on $\Sigma$, the transverse derivatives of $\phi$ blow up on $\mathcal C\mathcal H^+$; in fact, $\phi$ is not in…

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 $\mathcal{Q}^+$ 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.…

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…