6 problems

Let $\Sigma$ be a smooth manifold, let $ST^{\ast}\Sigma$ denote its unit cosphere bundle, and let $(f_t)_{t\in\mathbb R}$ be a positive path of contactomorphisms of…

A strongly asymptotically predictable spacetime $(M,g_{\mu\nu})$ has black hole region … where $J^-(\mathscr{I}^+)$ is the causal past of future null infinity and $\psi$ is the ass…

Nonexistence conjecture. There are quasilinear wave equations of the form $$ for which there exists initial data such that there does not exist any UGHD.

Let $M$ be a non-spacelike geodesically complete globally hyperbolic Lorentzian manifold with a compact Cauchy hypersurface of dimension $m \geqslant 3$. Suppose there is a positiv…

Let $F$ be the bundle whose sections define the relevant causal structures, and let $\mathrm{\Gamma}(F)$ be its space of sections with the Whitney fine $C^0$ topology. Write…

Let $C^\first$ and $C^{\first}$ be globally hyperbolic spacelike cone bundles over $M$ and $M'$, respectively, and let $\chi\colon M\to M'$ be an embedding inducing a chronological…