Pulsar timing and spacetime curvature

TL;DR

This paper investigates how weak gravitational waves influence pulsar timing, emphasizing gauge invariance, and establishes a direct link between pulsar timing signals and the Riemann tensor, aiding gravitational wave detection and alternative theories.

Contribution

It provides a gauge-invariant analysis of pulsar timing effects caused by gravitational waves, clarifying the roles of different contributions and their relevance to gravitational wave detection.

Findings

Doppler shift cannot be separated into gauge invariant gravitational and kinetic parts.

A gauge invariant separation relates the Doppler shift derivative to the Riemann tensor.

Gauge dependent effects are irrelevant for gravitational wave detection via pulsar timing.

Abstract

We analyze the effect of weak field gravitational waves on the timing of pulsars, with particular attention to gauge invariance, that is, to the effects that are independent of the choice of coordinates. We find: (i) the Doppler shift cannot be separated into gauge invariant gravitational wave and kinetic contributions; (ii) a gauge invariant separation can be made for the time derivative of the Doppler shift in which the gravitational wave contribution is directly related to the Riemann tensor, and the kinetic contribution is that for special relativity; (iii) the gauge dependent effects in the Doppler shift play no role in the program of gravitational wave detection via pulsar timing. The direct connection shown between pulsar timing and the Riemann tensor of the gravitational waves will be of importance in discussions of gravitational waves from alternative (non-Einsteinian) theories of gravitation.