Redshifts and Killing Vectors

TL;DR

This paper introduces the concept of Killing vectors in general relativity, explaining their properties and demonstrating their use in calculating gravitational and cosmological redshifts, enhancing understanding of symmetry in the theory.

Contribution

It provides an elementary introduction to Killing vectors and applies them to determine redshifts, which is rarely discussed in standard relativity courses.

Findings

Killing vectors are useful for analyzing symmetries in spacetime.

They can be employed to rigorously compute gravitational redshifts.

They also facilitate the understanding of cosmological redshifts.

Abstract

Courses in introductory special and general relativity have increasingly become part of the curriculum for upper-level undergraduate physics majors and master's degree candidates. One of the topics rarely discussed is symmetry, particularly in the theory of general relativity. The principal tool for its study is the Killing vector. We provide an elementary introduction to the concept of a Killing vector field, its properties, and as an example of its utility apply these ideas to the rigorous determination of gravitational and cosmological redshifts.