8 problems

Reiris' classification conjecture. Every three-dimensional vacuum static triple with non-empty boundary and $u$-complete ends is either the Schwarzschild solution or a flat solutio…

Cosmic No-Hair Conjecture. The only compact vacuum static triple with positive scalar curvature and connected boundary is the standard round hemisphere $\mathbb{S}^m_{+}$ with stat…

The examples under discussion are metrically complete static solutions in a fixed spatial topology, with electromagnetic matter restricted to magnetic energy. Garfinkle–Glass conje…

Let an asymptotically flat static perfect fluid spacetime be a solution satisfying the equations denoted by and. Fluid ball conjecture. Every such solution must be spherically symm…

Cosmological-horizon instability conjecture. Every horizon of cosmological type is necessarily unstable. In particular, every static solution to problem has at most one horizon of…

Dafermos–Holzegel conjecture. There are no static, globally regular asymptotically locally AdS solutions to the five-dimensional Einstein vacuum equations with topology…

A complete Riemannian manifold $(M^n,g)$ is a vacuum static space if it admits a nonzero smooth function $f$ satisfying … In dimension three, the known examples include flat tori…

Let $(\Sigma,g,N)$ be a complete solution of the Static Einstein equations with regular but possibly disconnected (non-empty) horizon $\partial\Sigma$. Suppose that the conformal m…