16 problems

Let an initial data set have a compact initial data surface, and let its maximal development be a spacetime whose spatial topology does not obstruct the existence of a maximal Cauc…

Let a space-time be represented by a collection of primordial point objects (PPOs), viewed as vertices, with a permutation symmetry expressing their democracy. Permutation-symmetry…

Kretschmann scalar conjecture. As $t\to+\infty$, the Kretschmann scalar becomes unbounded, including along spike timelines.

Let a spacetime evolve toward a singularity, and consider the dynamics of nearby observers. BKL conjecture. The dynamics of nearby observers should decouple near singularities. BKL…

Consider generic initial data for a suitable Einstein-matter system or for the Einstein vacuum equations, and let the maximal Cauchy development be the spacetime arising from those…

In a cosmological spacetime approaching a big bang singularity, the singularity is generic if it describes the typical behavior of solutions, spacelike if it is approached along sp…

Let an inhomogeneous cosmological model evolve toward a generic spacelike singularity, and consider its spatial points and a spatially homogeneous model describing the asymptotic d…

AVTD hypothesis. The quantity $(G^{-1}G_\tau)_\tau$ approaches zero as $\tau\to\infty$. This expresses that the leading asymptotic behavior is governed by the velocity-term-dominat…

Let a maximal Cauchy development arise from generic compact or asymptotically flat vacuum initial data. $C^0$-formulation of strong cosmic censorship. The maximal Cauchy developmen…

Let a maximal globally hyperbolic development be a spacetime arising from suitable Cauchy initial data for the Einstein equations, and let an extension be a strictly larger spaceti…

In a spacetime, causal geodesic incompleteness means that some causal geodesic cannot be extended to arbitrary values of its affine parameter; curvature blowup means that curvature…

In general spacetimes, a generic class of spacelike singularities is a class near which generic solutions of the Einstein field equations behave like spatially homogeneous spacetim…

In a singular spacetime approaching a final singularity, let $C$ denote the Weyl curvature tensor. Weyl curvature hypothesis. The Weyl tensor becomes unbounded as one approaches th…

Let a vacuum initial data set determine its maximal globally hyperbolic development, meaning the maximally extended spacetime determined by the initial data within which causality…

Weak BKL conjecture. As the singularity is approached, the equations of motion can be well approximated by those of the truncated theory in the vicinity of the singularity. This is…

Let ${}^4M$ be a four-manifold foliated by spatial leaves $M_t$, with basic variables $(C_i{}^j,P_i{}^j)$, lapse $N$, and shift $N^i$. Let $D_i$ denote the spatial derivative opera…