20 problems

Let $(X,g)$ be a globally hyperbolic spacetime, and let $\mathcal{N}$ be its space of null geodesics. For each point $p\in X$, write $\operatorname{sky}_p$ for its sky, viewed as a…

Let $M$ be a globally hyperbolic spacetime, let $\mathcal{N}$ be its manifold of cone geodesics, and for each event $x\in M$ let … be its sky. Low's sky-linking conjecture. Causal…

Let $(\mathsf{M},g)$ and $(\mathsf{M}',g')$ be the spacetimes under consideration. For each $k\in\boldsymbol{\mathrm{N}}$, let $\nu^k$ and $\nu'^k$ be the corresponding probability…

A spacetime is a pair $(M,g)$, where $M$ is a differentiable manifold and $g$ is a smooth, symmetric, non-degenerate $(0,2)$-tensor field. Two spacetimes are isocausal when there a…

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…

Time-machine conjecture. Given a suitable opportunity, the civilization can succeed in creating a time machine.

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 have a Morse function whose critical points may be highly anisotropic, meaning that the coefficients in its local quadratic form can have ratios far from $71$…

Let a Morse spacetime be a singular Lorentzian spacetime with isolated critical points where the Lorentz metric degenerates and spatial topology changes. Sorkin's conjecture. Causa…

Let $(M,g)$ be a globally hyperbolic spacetime and let $t:M\to\mathbb{R}$ be an admissible time function, meaning a time function satisfying the conditions in Definition. Admissibl…

Causal simplicity conjecture. Every strongly causal null pseudoconvex space-time is causally simple.

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 $f$ and $g$ be test functions for smeared fields $\phi(f)$ and $\phi(g)$ in a real scalar quantum field theory. An ideal measurement of a smeared field is an ideal measurement…

Let $(M,\mathbf{g})$ be a spacetime and let $\tau$ be a generalized time function that may be locally anti-Lipschitz but is discontinuous along any causal curve. A distance in…

A spacetime is considered together with a fixed topology that supplies its topological properties and influences its geometric description. Dynamical-topology conjecture. The chall…

Exhaustion conjecture. The topologies described in Theorem 2 exhaust all possible spacetime topologies belonging to the class $\mathfrak{Z}-\mathfrak{G}$ that admit a countable bas…

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…

Let $({X}^{m+1},g)$ be a globally hyperbolic spacetime whose Cauchy surface is diffeomorphic to an open subset of $\mathbb R^m$. When $m=2$, let $x,y\in X$ be events and let…