6 problems

Let $(\widetilde{M}, \widehat{g})$ be a globally hyperbolic Lorentzian manifold with compact Cauchy hypersurfaces. Say that late-time observers are oblivious to topology if there e…

Let a Morse spacetime be a singular Lorentzian spacetime built from a Morse function, whose critical points have an index and a coindex. Borde–Sorkin conjecture. A Morse spacetime…

Let $(\mathcal{M},h,f,\zeta)$ be a Morse geometry of dimension $n$, and let $(M,g)$ be the corresponding Morse spacetime. Assume that $f$ has a single critical point for each criti…

Let $\mathcal{M}$ be a compact cobordism of dimension $n$, $h$ a Riemannian metric, $\zeta>1$ a constant, and $f$ a Morse function. Let…

Let $(M,g_{ab})$ be an inextendible, hole-free, vacuum solution. A spacetime is strongly causal if every point $p$ and neighborhood $O$ of $p$ have a neighborhood $V\subseteq O$ th…

Let $(\Sigma, h_{ab}, k_{ab})$ be an initial data set with $\Sigma$ three-dimensional. A spacetime is strongly causal if every point $p$ and neighborhood $O$ of $p$ have a neighbor…