Linking and causality in (2 + 1)-dimensional static spacetimes

Abstract

Given a (d + 1)-dimensional spacetime (M, g), one can consider the set N of all its null geodesics. If (M, g) is globally hyperbolic then this set is naturally a smooth (2d − 1)-manifold. The sky of an event x ∊ M is the subset X = {γ ∊ N : x ∊ γ} and is an embedded submanifold of N diffeomorphic to Sd−1. Low conjectured that if d = 2 then x, y ∊ M are causally related iff X, Y ⊂ N are linked (in an appropriate sense). We prove Low's conjecture for a (large) class of static spacetimes.