7 problems

Let $(M,g)$ be a globally hyperbolic, timelike geodesically complete spacetime with compact Cauchy surfaces satisfying the strong energy condition. For a Cauchy temporal function…

Let $M$ be a stably causal Lorentzian manifold whose sectional curvatures are much less than $1$, and let $\gamma$ be a timelike curve from $s$ to $t$ in $M$ whose radius of curvat…

Let $(M,g)$ be a globally hyperbolic $(3+1)$-dimensional spacetime with a Cauchy surface diffeomorphic to a subset of $\mathbb{R}^3$, and let $N$ be its manifold of light rays. For…

Let $(M,g)$ be a globally hyperbolic, timelike geodesically complete spacetime with compact Cauchy surfaces satisfying the strong energy condition. For a Cauchy temporal function…

A spacetime is considered together with its directed completion, obtained by adjoining ideal elements determined by the directed-completeness construction, and with the completion…

Let $\mathcal{X}$ be a globally hyperbolic spacetime whose Cauchy surface is not homeomorphic to the sphere. Let $x,y\in\mathcal{X}$ be causally related points, and consider future…

Causal Legendrian-linking conjecture. Assume that one cannot put a $Y^x_{\ell}$ Riemann metric on the Cauchy surface $M$. Then two events $x,y\in X$ are causally related if and onl…