2 Lensing in Arbitrary
Spacetimes
By a spacetime we mean a 4-dimensional
manifold
with a (
, if not otherwise stated)
metric tensor field
of signature
that is
time-oriented. The latter means that the non-spacelike vectors make
up two connected components in the entire tangent bundle, one of
which is called “future-pointing” and the other one
“past-pointing”. Throughout this review we restrict to the case
that the light rays are freely propagating in vacuum, i.e., are not
influenced by mirrors, refractive media, or any other impediments.
The light rays are then the lightlike geodesics of the spacetime
metric. We first summarize results on the lightlike geodesics that
hold in arbitrary spacetimes. In Section 3
these results will be specified for spacetimes with conditions on
the causal structure and in Section 4 for spacetimes with
symmetries.