Behavior of spacelike geodesics in the extended Schwarzschild manifold

We demonstrate that there exist unstable, spacelike, circular orbits in the Schwarzschild field for all radii in the range 0<r<3m. The conditions under which spacelike trajectories bend toward or away from the source of the field are derived for the entire r-φ plane. We show that any nonradial spacelike geodesic with turning point less than 2m will appear spacelike over the entire u-v plane. The scattering and capture cross sections for a particle on a spacelike trajectory are evaluated. Finally, we suggest that there are compelling reasons for rejecting the usual assumption of a global past-future relation in the extended Schwarzschild manifold.