The gravitational light shift and the Sachs-Wolfe effect

TL;DR

This paper derives a new, general formula for gravitational light shifts applicable to various spacetimes, and applies it to analyze the Sachs-Wolfe effect in cosmology, enhancing understanding of cosmic microwave background anisotropies.

Contribution

It introduces a novel, general formula for gravitational light shifts that does not rely on Killing fields, expanding analytical tools in gravitational physics.

Findings

The formula is applicable to a wide range of spacetimes.

It provides new insights into the Sachs-Wolfe effect in cosmology.

Illustrations demonstrate the formula's usefulness in practical scenarios.

Abstract

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.