Figure 7: Thin bundle around a ray in a
spherically symmetric static spacetime. The picture is purely spatial, i.e., the time coordinate
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 , and the tangential diameter of the cross-section gives the tangential
angular diameter distance . In contrast to the
general situation of Figure 3, here the
angle is zero (if the
Sachs basis is
chosen appropriately). Recall
that and are positive up to the first
caustic point.
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