= Causal projection along a spacelike circular fiber
For $g=q+C(d\psi+A)^2$ with $C>0$, projection of every causal curve is causal for $q$, since $q(\dot\gamma,\dot\gamma)\leq g(\dot\gamma,\dot\gamma)\leq0$. Conversely, the lift defined by $d\psi=-A$ along any given base curve has the same norm as that curve. Thus the orbit-space metric $q$ describes the projected causal structure exactly. A <Penrose diagram> suppressing that circle is a quotient diagram, not the metric of a constant-$\psi$ slice.
Back to article page
