6 problems

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…

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…

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

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

Large-data local BV scattering conjecture. There exists initial data of arbitrarily large BV norm whose maximal global development scatters locally in the BV norm.