6 problems

Consider an asymptotically flat spacetime arising from initial data for the Einstein equations, with an exterior region containing a black hole. Final state conjecture. At late tim…

Black hole settling-down conjecture. At $\Sigma_{t'}$, with $t'\gg t$, the spacetime will be described by a stationary metric. This is a dynamical black-hole statement: after black…

For a geodesic polygon in a black-hole spacetime, let $\mathring{\alpha}_{M}$ denote its Gaussian bending measure, and suppose that all vertices lie at the same distance $d$ from t…

Extension conjecture for stationary spacetimes. These results can be extended to massless test fields propagating on stationary spacetimes, including the Schwarzschild spacetime.

Let $Z$ be a spatially compact stationary globally hyperbolic spacetime, and let $D_Z$ have discrete spectrum in $\operatorname{Char}(\Box)$ with eigenvalue counting function … Ass…

Converse characterization. Randers metrics of constant flag curvature are precisely those whose associated spacetime of the Randers form is conformally flat.