20 problems

Let the Einstein–Maxwell-charged-scalar-field system be given by equations … , and consider generic, one-ended, asymptotically flat, complete spherically symmetric initial data. It…

Let $B$ be a spatial region and let $C$ denote its circumferential radius. Thorne's hoop conjecture. A horizon will be present within $B$ if the mass within $B$ exceeds the mass of…

Massless-field gravitational collapse can exhibit black-hole formation, critical solutions, self-similarity and mass scaling. A supercritical evolution PDE is an evolution partial…

Let $\alpha$ be the dimensionless coupling constant, and let $\alpha_0<\alpha_1$ denote the parameter values associated with the CSS solutions. Let the $n=1$ solution be the contin…

Let $D_v$ denote the covariant derivative in the interior null direction $v$, let $\phi$ be the scalar field, and consider solutions of equations … . A quantity is oscillatory towa…

Consider generic regular spherically symmetric one-ended asymptotically flat black hole solutions of the Einstein–Maxwell-charged-scalar-field equations 1.1\–5.1\ with…

Let a black hole form from generic gravitational collapse, and denote its terminal boundary's Cauchy horizon by $\mathcal{CH}_{i^+}$ and its spacelike singularity by $\mathcal{S}$.…

A black string in $4+1$ or higher spacetime dimensions is subject to the Gregory–Laflamme instability, in which perturbations breaking translation symmetry along the string lead to…

Let $B$ denote the magnetic component of the Weyl curvature relative to a unit timelike vector, and let $A_B$ and $L_B$ denote its amplitude and wavelength scales. Magnetic short-p…

Consider a generic solution of the vacuum Einstein equations describing gravitational collapse, and interpret a Kerr black hole as a rotating stationary vacuum black-hole solution.…

In the Einstein-dust system, naked singularities are singularities whose signals can be received by asymptotic observers. Cosmic censorship hypothesis. Such singularities should be…

Let $g$ be a spacetime metric satisfying the vacuum Einstein equations … A Cauchy datum is regular and one-ended when it is regular and has one asymptotically flat end, and gravita…

Apparent-horizon existence conjecture. The smooth spacelike apparent horizon exists in gravitational collapse and arises from general, both isotropic and anisotropic, initial data.

Let a generic gravitational collapse produce an asymptotically flat vacuum black hole spacetime, with the exterior geometry considered relative to the family of Kerr black hole sol…

Let $\mathcal{Q}^+$ be the quotient spacetime, $\mathcal{I}^+$ future null infinity, and let the black-hole asymptotic charge mean the limiting charge appearing in the model. Nonze…

Let $\mathcal{Q}^+$ be the quotient spacetime, $\mathcal{I}^+$ future null infinity, and interpret “sub-extremal in the limit” as the limiting black-hole condition stated in the pa…

Let $\mathcal{Q}^+$ be the quotient spacetime, $\mathcal{I}^+$ future null infinity, and $\mathcal{S}$ the relevant singular boundary component. Space-like singularity conjecture.…

Let $\mathcal{Q}^+$ be the quotient spacetime, $\mathcal{I}^+$ future null infinity, $\mathcal{S}$ the non-central $r=0$ boundary component, $\mathcal{CH}_{i^+}$ the Cauchy horizon…

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

In a $3+1$-dimensional spacetime satisfying the Einstein vacuum equations … an apparent horizon is the boundary where outward-directed light rays cannot move outward. Ashtekar's ap…