42 problems

Consider smooth developments of the Einstein–Maxwell–Klein–Gordon system as in Theorem 1.1, with coupling parameter $\mathfrak{e}\neq 0$. Let $\mathcal{Q}^+$ be the quotient spacet…

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…

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…

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…

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

Let $(\Sigma,\leftidx{^\Sigma}{\mathbf{g}}{},\leftidx{^\Sigma}{\mathbf{K}}{},\mu,J)$ be generic asymptotically flat initial data, and let $(M,\mathbf{g})$ be its maximal globally h…

Let $(\Sigma,\leftidx{^\Sigma}{\mathbf{g}}{},\leftidx{^\Sigma}{\mathbf{K}}{},\mu,J)$ be generic asymptotically flat initial data, and let $(M,\mathbf{g})$ be its maximal globally h…

Let asymptotically flat initial data for Einstein's field equations be given, and let its maximal development be the corresponding spacetime. A future null infinity $\mathcal{I}^+$…

Let $\Sigma$ be a regular, compact spacelike hypersurface without boundary. Prescribe generic initial data in the spherically symmetric class for the Einstein-Maxwell-charged-Klein…

Let $(M,g)$ be a spacetime and define … A causal geodesic is future incomplete if it cannot be extended to arbitrarily large future parameter values. Volumetric WCC. In a generic p…

Let $(M,g_{ab})$, $S$, $D(S)$, $\mathscr{A}$, $\mathscr{B}$ and $\omega$ be as in the quantum strong cosmic censorship conjecture, and suppose that $(D(S),\omega)$ satisfies the se…

Let $S$ be a strictly partial Cauchy surface of the (not necessarily globally hyperbolic) spacetime $(M,g_{ab})$, and let $D(S)$) be its domain of dependence. Regard…

Let $S$) be a strictly partial Cauchy surface of the (not necessarily globally hyperbolic) spacetime $(M,g_{ab})$, and let $D(S)$ be its domain of dependence. Regard…

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 $(M,g)$ be a generic, maximal, physically admissible spacetime admitting a complete spacelike hypersurface $\Sigma$. Let $D^+(\Sigma)$ denote its future domain of dependence, l…

Let $\mathcal P$ be the parameter space of dimensionless Kerr--AdS black hole parameters $(\mathfrak m,\mathfrak a):=(M\sqrt{-\Lambda},a\sqrt{-\Lambda})$. Let…

Let $\psi$ be a linear perturbation solving the wave equation on Reissner--Nordström--AdS or Kerr--AdS, arising from generic Cauchy data with Dirichlet boundary conditions imposed…

Let $\boldsymbol{\psi}$ be a linear perturbation solving the wave equation on a subextremal asymptotically AdS black hole, with generic initial data and Dirichlet or more general b…

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…

Let $g$ be the maximal globally hyperbolic development of generic regular data for the Einstein–Maxwell–Klein–Gordon system … where $D=\nabla+iq_0A$. $C^0$ Strong Cosmic Censorship…

Let $(\mathcal{M},g)$ be an asymptotically flat solution of the Einstein vacuum equations … An event horizon is the boundary separating the region from which observers can reach in…

Let $(M,g_{ab})$ be an inextendible, hole-free, vacuum solution. A spacetime is strongly causal if every point $p$ and neighborhood $O$ of $p$ have a neighborhood $V\subseteq O$ th…