The global hyperbolicity conjecture for physical spacetimes

A strongly asymptotically predictable spacetime $(M,g_{\mu\nu})$ has black hole region

$$B=M\backslash \psi^{-1}[J^-(\mathscr{I}^+)],$$

where $J^-(\mathscr{I}^+)$ is the causal past of future null infinity and $\psi$ is the associated conformal isometry. Global hyperbolicity conjecture. All physical spacetimes are globally hyperbolic. Global hyperbolicity excludes important causal pathologies and supports the formulation of black hole regions and Cauchy evolution; the source gives no resolution status for this assertion.