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

Generic outgoing-energy conjecture. Spherically symmetric solutions should be the only isolated solutions for which the energy $M_2(\tau)$ is constant.

Let $\mathcal{A}$ be the set of spherically symmetric marginally trapped spheres, let $v$ be the null coordinate used in the paper, and let $V$ be sufficiently large. Achronality c…

A static perfect fluid solution is asymptotically flat if its spacetime approaches a flat spacetime at infinity, and it is spherically symmetric if it is invariant under rotations…

Let $X$ be a random vector in $\mathbb{R}^d$, and let $d$ independent random projection directions be sampled. In dimension two, agreement between the projections of a distribution…

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…

Affine Schwarzschild conjecture. The solution to this case is given by an affine generalisation of Schwarzschild geometry with cosmological constant.

Let $\mathcal{CH}_{\Gamma}$ denote the Cauchy horizon emanating from the center in the one-ended spherically symmetric collapse setting. Generic absence of a central Cauchy horizon…

Let $\mathcal{CH}_{i^+}$ be a dynamical Cauchy horizon, let $S_0$ be the set of static points on it, and call a point a Dafermos point when it lies in…

Let a Cauchy horizon be a null boundary on which the area radius $r$ remains bounded away from zero. Cauchy-horizon $C^0$ extendibility conjecture. Such Cauchy horizons are always…

Consider the Einstein–scalar-field model obtained by setting $F\equiv0$ in the displayed Einstein–Maxwell–Klein–Gordon system and taking $m^2=0$. Christodoulou continuous inextendi…

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

Consider spherically symmetric admissible Cauchy initial data with non-vanishing charge and compactly supported initial scalar field, and let their maximal globally hyperbolic futu…

Non-symmetric scattering conjecture. The spherical symmetry assumption can be removed from this theorem. The theorem is established for spherically symmetric data, but the correspo…