94 problems

Let $(\mathcal{M},g)$ be a $3+1$-dimensional Lorentzian spacetime solving the Einstein field equations, arising as the maximal future development of generic, regular, asymptoticall…

Let $(\mathcal{M},\mathbf{g})$ be the maximal development of generic asymptotically flat initial data for Einstein's vacuum field equations. Weak cosmic censorship conjecture. The…

The strong cosmic censorship conjecture concerns the interiors of generic black-hole spacetimes and the possibility of extending their spacetime metrics beyond the Cauchy horizon.…

Consider generic, non-spherically-symmetric solutions of the Einstein-scalar-field system arising from gravitational collapse, and let their Maximal Globally Hyperbolic Development…

Let $(M,g)$ be the maximal future development of generic asymptotically flat initial data. A terminal indecomposable past set is a past set $\mathcal{P}$ in $M$ of the type describ…

Let $(\mathcal{M},\overline{g})$ be the maximal Cauchy development of complete, generic vacuum initial data lacking trapped or marginally trapped surfaces. Let $\mathcal{J}^+$ be i…

Let $\mathcal{Q}^+$ be the quotient of the maximal future development, $J^-(\mathcal{I}^+)$ the causal past of future null infinity, $\mathcal{A}$ the apparent horizon, and…

Let $\mathcal{I}^+$ denote future null infinity, and consider the admissible data in the one-ended spherically symmetric Einstein–Maxwell–Klein–Gordon model. Weak Cosmic Censorship…

Strong cosmic censorship conjecture. For suitable initial data, the MGHD is generically inextendible.

Let $(\mathcal M,g)$ be the maximal vacuum Cauchy development of sufficiently small perturbations of asymptotically flat two-ended Kerr data with parameters $0<|a|<M$. Ori's conjec…

Let $(\Sigma,h)$ be a connected Riemannian $3$-manifold and let $\sigma$ be a symmetric two-covariant tensor satisfying the compatibility conditions of a second fundamental form. L…

Let $(M^3,g,h)$ be asymptotically flat Cauchy data satisfying $\mu \ge |J|$, and suppose the Einstein evolution from these data has the global properties described in the Penrose a…

Let $b\Sigma,\stackrel{\circ}{g},K,E_i,B_i,\stackrel{\circ}{\phi},\phi'\d$ be a complete asymptotically flat initial data set for the Einstein–Maxwell–scalar field system, with asy…

Consider generic initial data for a suitable Einstein-matter system or for the Einstein vacuum equations, and let the maximal Cauchy development be the spacetime arising from those…

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

Consider spherically symmetric initial data for the Einstein-scalar field equations in the regularity class $\mathcal{B}$, and let their maximal globally hyperbolic development (MG…

Let the maximal globally hyperbolic development (MGHD) be the spacetime arising from regular initial data for the Einstein equations coupled with a reasonable matter model. Initial…

Strong cosmic censorship conjecture. Maximal globally hyperbolic developments solving the Einstein equations with generic and suitably regular initial data are inextendible.

Consider generic initial data giving rise to a perturbation of a Kerr black hole governed by the Einstein vacuum equations, and let the perturbed spacetime have a Cauchy horizon. I…

Universal black-hole inequality conjecture. The mass should satisfy

Let $\mathcal{S}={r=0}$ denote the spacelike component of the terminal boundary in the spherically symmetric black-hole solutions considered in the paper. $C^0$-inextendibility con…

Let $(\widetilde{M}, \widehat{g})$ be a smooth, time-oriented, globally hyperbolic Lorentzian $(3+1)$-dimensional spacetime with $\widetilde{M} \cong M \times \mathbb{R}$, where…

Consider generic, non-spherically-symmetric solutions of the Einstein-scalar-field system describing black-hole interiors, and let $\mathcal{S}$ denote a terminal singularity. Gene…

Generic oscillation conjecture. The oscillation condition is satisfied for generic solutions of the Einstein equations and the Einstein–Maxwell-charged-scalar-field system. Such an…

The Oppenheimer–Snyder spacetime is the spherically symmetric dust model of gravitational collapse, whose exterior agrees with the Schwarzschild metric and which terminates at a sp…