9 problems

Consider a generic gravitational-collapse scenario in which a scalar field evolves in the spacetime generated by Cauchy initial data. Let the scalar field's decay along the event h…

Consider relativistic scalar field models $phi^4_n$ with $n\geq 5$, and more generally nonrenormalizable interactions such as $phi^6_n$ with $n\geq 4$. In the ultralocal theory, ad…

Let $(\mathcal M,g,F,A,\phi)$ be a black hole solution of the Einstein–Maxwell–Klein–Gordon system arising from generic, spherically symmetric smooth Cauchy data on an asymptotical…

Let $\mathcal{H}^+$ be the event horizon and let $v$ be the standard advanced time null coordinate. Massive scalar-field tail conjecture. For smooth, regular, generic admissible da…

Charged massless scalar decay conjecture. For smooth, regular, generic admissible data with a non-empty black hole and $m^2=0$,

Hod–Piran sharp decay conjecture. In the charged massless case, the scalar field is expected to satisfy

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 $\mathcal A$ denote the class of initial data such that the corresponding maximal globally hyperbolic developments are future causally geodesically complete solutions to the Ei…

Let $\Phi_\ell$ be the scalar field mode of angular momentum $\ell$, let $D^{(\ell)}_{i_1,i_2,\cdots,i_\ell}$ be the differential operator appearing in the ladder-operator construc…