19 problems

Strong cosmic censorship conjecture. For suitable initial data, the MGHD is generically inextendible.

Strong cosmic censorship conjecture. Maximal globally hyperbolic developments solving the Einstein equations with generic and suitably regular initial data are inextendible.

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…

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…

Let $(M,g)$ be a space-time, and let $(c,x)$ be a pair consisting of a singular curve and a point as in the source's definition of a locally naked singularity, so that…

In a spacetime satisfying reasonable physical assumptions, let $S$ be a complete spacelike hypersurface and let $H^+(S)$ denote its future Cauchy horizon. Strong cosmic censorship…

Let $(M,g)$ be a Lorentzian manifold with $M=\mathbb{R}\times\Sigma$ and metric tensor … For each $t\in\mathbb{R}$, let $(\Sigma_t,g_{\Sigma_t})$ denote the Riemannian manifold ind…

Weak Cosmic Censor Conjecture. The domain of outer communication $\mathcal{D}(\tilde{M})$ is globally hyperbolic. This is the mathematical formulation given for the weak cosmic cen…

A spacetime may have an initial singularity, such as a big-bang singularity, and may contain black or white holes. The region away from these holes is the portion not hidden inside…

A spacetime is a Lorentzian manifold $(M,g)$, and it is globally hyperbolic when it satisfies the standard causality and compactness conditions ensuring well-posed causal evolution…

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

Asymptotically Minkowski time-function conjecture. Assumptions $({\rm aM})$ i) and iii) should imply assumption $({\rm aM})$ iv): there exists a time function $\tilde t$ such that

Let $M={\mathbb R}^{1+d}$ carry a Lorentzian metric $g$, and suppose that $(M,g)$ is globally hyperbolic. Let $\eta$ be the Minkowski metric, and assume … Here…

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…

Let the maximal development of asymptotically flat initial data for the vacuum Einstein equations be the globally hyperbolic spacetime determined by the data. Strong cosmic censors…

Let $M$ be a globally hyperbolic stationary Lorentzian manifold. The Riemannian result under discussion asserts the existence of infinitely many closed geodesics on compact Riemann…