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. 
Cesar Merlin and Marcelo Salgado
gr-qc astro-ph.CO hep-th