114 problems

Let an expanding universe have a positive cosmological constant. Cosmic no-hair conjecture. All such universes asymptotically admit the de Sitter universe as a solution. This conje…

Penrose's Weyl curvature hypothesis. The Weyl curvature tensor should remain finite at the initial singularity, while the Ricci tensor should be singular there.

Cosmic no-hair conjecture. The only $n$-dimensional compact static triple $(M^n,g,f)$ with positive scalar curvature and connected boundary $\Sigma$ is a round hemisphere…

A $G_{2}$ cosmology is a spacetime admitting two commuting spacelike Killing vector fields and satisfying the Einstein field equations with a perfect-fluid source. Its dynamical eq…

Let cosmological solutions to Einstein's equations have a positive cosmological constant. Cosmic no-hair conjecture. Generic cosmological solutions generally asymptote to de Sitter…

Let $(M,\mathcal{C})$ be a Riemann-Lorentz conformal space with polar end $D^{\infty}$. Suppose that $D^{\infty}$ is conformal-flat. A simultaneity distribution is a distribution w…

Periodic-boundary-condition vacuum-energy conjecture. Periodic boundary conditions select the field component of the vacuum energy, equal to $\varepsilon_f$ up to a factor; this co…

Let such a cosmological spacetime have compact Cauchy surfaces. A constant mean curvature (CMC) Cauchy surface is a Cauchy surface whose mean curvature is constant, and a foliation…

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…

Consider the setting of Theorem … , the spacetime is future causally geodesically complete. The surrounding discussion says that the answer is expected to be affirmative for…

Let $k$ be the curvature of the symmetric surfaces, let $\Lambda$ be the cosmological constant, and consider generic initial data for the surface-symmetric Einstein-Vlasov system.…

Nonexistence conjecture. There are no values of $n$ for which a solution exists.

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

Attracting silent-boundary subset conjecture. The set ${\mathcal U}_{\rm vac}^{-}$ forms an attracting subset that organizes the oscillatory dynamics of generic timelines approachi…

A spacetime is maximally extended if it admits no further extension, and it is globally hyperbolic if it has a Cauchy surface. A constant mean curvature (CMC) hypersurface is a spa…

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…

The model uses an FRW equation of state intended to agree with that of the standard cosmological model after radiation decouples from matter. Uniform-expansion conjecture. If the e…

Let $(\mathcal{M},\mathbf{g})$ be a four-dimensional spacetime satisfying the Einstein field equations, and let the variational condition … selects the conformally regular four-geo…

Let $\mathfrak{q}\in[0,1]$, and consider the massless Boltzmann equation with scattering kernel … on an FLRW spacetime, with Maxwell--Jüttner equilibrium $J(t^{2\mathfrak{q}}p)$ an…

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 $d\geq 3$, and consider solutions of quantum gravity in $d$ spacetime dimensions. A cosmological event horizon is the horizon associated with the finite distance traveled by li…

Let $\mathfrak{T}$ denote the energy--momentum distribution function in the Finsler-gravitational field equations, and let the Landsberg tensor describe the corresponding anisotrop…

Consider a Finslerian spacetime geometry whose Lagrangian depends on direction and whose gravitational field includes the contribution of the velocity distribution of a many-partic…

Spikes conjecture. Spikes form the non-local part of the generalized Mixmaster attractor.

Consider physically relevant matter models coupled to the Einstein equations with positive cosmological constant, including the Einstein–$\Lambda$–Maxwell and Einstein–$\Lambda$–Eu…