The gravitational light shift and the Sachs-Wolfe effect
  Using a 3+1 decomposition of spacetime, we derive a new formula to compute
the gravitational light shifts as measured by two observers which are normal to
the spacelike hypersurfaces defining the foliation. This formula is quite
general and is also independent of the existence of Killing fields. Known
examples are considered to illustrate the usefulness of the formula. In
particular, we focus on the Sachs-Wolfe effect that arises in a perturbed
Friedman-Robertson-Walker cosmology.
