19 problems

Smooth-data naked singularity conjecture. There exist naked singularities arising from smooth data on $\partial\mathfrak{M}_{\mathrm{black}}\cap\partial\mathfrak{M}_{\mathrm{non}}$…

Let $\widehat{\mathfrak M}$ be a moduli space of Cauchy data on $\mathbb R^3$ for a matter-model and symmetry-class combination in which an exact extremal Kerr--Newman event horizo…

Let the moduli space of solutions of the Einstein equations contain asymptotically extremal Reissner--Nordström black holes, and let the black hole formation threshold be the bound…

The examples under consideration are fine-tuned one-parameter families of smooth, spherically symmetric solutions exhibiting extremal critical collapse, meaning critical collapse i…

Extremal critical collapse is the scenario in which a threshold solution separating dispersion from collapse settles to an extremal black hole without trapped surfaces in the relev…

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…

A discretely self-similar (DSS) solution is a solution invariant under a discrete scale transformation. An unstable mode is a perturbation mode that grows away from the solution, a…

In the Einstein–Yang–Mills system considered here, the intermediate regime exhibits episodes of approximate continuous self-similarity (CSS) within an overall discretely self-simil…

Let $\kappa$ be the dimensionless curvature parameter of the constant-curvature target manifold, and let $\Delta$ denote the echoing period of a discretely self-similar (DSS) solut…

Let $\Lambda<0$ be a negative cosmological constant, and let the gluing solution consist of the $q=4$ Garfinkle continuously self-similar interior joined to a Vaidya exterior. A so…

Consider a smooth one-parameter family of smooth, asymptotically flat initial data, with parameter $p$, and let $p_*$ denote the black-hole threshold. Near threshold, the black-hol…

Massive scalar electrodynamics has gauge coupling $e$ and mass $m$, and a universality class is the collection of theories with the same critical behavior. Type II critical phenome…

Consider vacuum gravitational collapse, governed by … The rotating extremal Kerr solution plays the role of extremal Reissner–Nordström. Vacuum extremal-collapse conjecture. Extrem…

Consider the spherically symmetric Einstein–Maxwell system coupled to a massless charged scalar field. Charged-scalar extremal-collapse conjecture. Extremal critical collapse occur…

Let $\mathfrak B$ be the black-hole region in the moduli space and let $\mathfrak B_\mathrm{crit}$ denote the critical codimension-one submanifold. For some $\varepsilon>0$ and…

Consider the moduli space $\mathfrak M$ of the spherically symmetric Einstein–Maxwell–Vlasov system for particles of mass $\mathfrak m$, and let $\{\Psi_\lambda\}$ be an interpolat…

The Einstein–Maxwell–Vlasov system admits examples of critical collapse with a suitable codimension-one property in the moduli space of initial data. This is the expected structure…

Universality conjecture. The exponent $\gamma$ ought to be universal for four-dimensional gravity coupled to any matter content.