15 problems

A high-frequency limit is a spacetime obtained as the limit of a sequence of vacuum spacetimes. The massless Vlasov system is the Einstein–Vlasov system in which the Vlasov matter…

Let $k$ be the curvature of the symmetric surfaces and let $\Lambda$ be the cosmological constant. Consider surface-symmetric cosmological spacetimes with collisionless matter and…

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 $\mathcal{H}^+$ be the future event horizon and let … is satisfied on $\mathcal{H}^+$. This is stated as a stronger conjecture implying the absence of future Cauchy horizons; t…

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.…

In the spherical Einstein–Maxwell–charged Vlasov system, let eRN denote an extremal Reissner–Nordström black hole, and let a critical black hole be the threshold solution separatin…

Consider spherically symmetric Einstein–Vlasov collapse with massless particles and smooth initial data. A threshold solution is a solution on the boundary between dispersal and bl…

Casimir-binding-energy stability conjecture. If $f_0$ satisfies the CBEC, then $f_0$ is stable with respect to mass-preserving perturbations.

Let $Phi$ be a fixed energy profile function satisfying suitable regularity assumptions, and let $kappa>0$ be the redshift factor parametrizing compactly supported steady states of…

Burnett's conjecture. There is a finite, non-negative Radon measure $\bm\mu$ on $\bm{T^*\mathcal M}$ such that $(\bm{\mathcal M},\bm g,\bm\mu)$ is a solution of the Einstein--massl…

Compactness conjecture. The compactness ratio for any shell surrounding a black hole satisfies

Cosmic no-hair conjecture. The spacetime appears de Sitter like to late-time observers.

Consider a sequence of steady-state, spherically symmetric Einstein–Vlasov solutions, with total rest mass $M_0$, ADM mass $M$, binding energy $e_b=M_0-M$, and fractional binding e…

In a spherically symmetric Einstein–Vlasov spacetime, consider initial data whose evolution is studied in a time gauge for which global existence would rule out naked singularities…

Let a steady-state sequence be a one-parameter family of spherically symmetric static solutions of the Einstein–Vlasov system, and let the fractional binding energy of a steady sta…