16 problems

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…

Holographic screen conjecture. The holographic screen should be the appropriate analogue of the AdS boundary for a holographic description of general spacetimes.

Entanglement–geometry conjecture. Quantum entanglement is necessary for connected spacetime geometry.

Let $n \geq 3$ and let $M$ be a cNTV $n$-dimensional spacetime. Write \langle M, \mathrel{\scalebox{0.85}{oldalpha}} \rangle for its frame with the causal relation…

Let a stationary black hole be characterized by its mass, spin, and electric charge. No-hair conjecture. All stationary black holes are diffeomorphic to the Kerr--Newman spacetime…

Higher-dimensional spacetime density conjecture. There exists an integer $m\geq 2$ such that, for every $\epsilon>0$, there exists a positive integer $d$ with the property that whe…

Let the sequence of warped product spacetimes in Example … with the taxi space portion removed. The conjecture concerns the discrepancy between Gromov–Hausdorff and Sormani-Wenger…

The spacetime manifold is endowed with a projective structure by the principle of universality of free fall, meaning an equivalence class of curves up to reparametrization, and wit…

In the setting of spacelike slices, Sormani–Wenger intrinsic flat convergence (SWIF convergence) is the convergence of metric spaces obtained from spacelike slices of spacetimes. L…

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

Let a spacetime be asymptotically $AdS_2 \times S^2$ and satisfy the null energy condition, or more generally the averaged null energy condition. Maldacena's conjecture. Any such s…

The authors consider quantum mechanical systems on a fixed type of spacetime geometry, allowing the involved particles to have different spins. Universality conjecture. The influen…

The category of spacetimes is studied using chains of Cauchy wedges, with its connected components labelled by equivalence classes of Riemannian manifolds of dimension $n-1$, modul…

Boost non-invariance conjecture. The spacetime interval is not invariant under boosts for $N\geq 3$; in particular, under an infinitesimal boost one obtains

The spacetime under consideration satisfies the hypotheses of Theorem … is weakly ultimately Schwarzschildean to order $k+2$. This conjecture is motivated by techniques that obtain…

Let the initial data be generic compact or asymptotically flat data for a suitable Einstein–matter system, and let its maximal Cauchy development be the corresponding maximal globa…