Figure 7

Figure 7: Thin bundle around a ray in a spherically symmetric static spacetime. The picture is purely spatial, i.e., the time coordinate t is not shown. The ray is contained in a plane, so there are two distinguished spatial directions orthogonal to the ray: the “radial” direction (in the plane) and the “tangential” direction (orthogonal to the plane). For a bundle with vertex at the observer, the radial diameter of the cross-section gives the radial angular diameter distance D+, and the tangential diameter of the cross-section gives the tangential angular diameter distance D -. In contrast to the general situation of Figure 3, here the angle x is zero (if the Sachs basis (E ,E ) 1 2 is chosen appropriately). Recall that D+ and D - are positive up to the first caustic point.