Proper Time Shifts in Pulsar Timing Arrays

Abstract

Pulsar timing arrays are a powerful tool for probing low-frequency gravitational phenomena and physics beyond the Standard Model. We establish a general, gauge-invariant framework for the timing residual by identifying the measurable quantity as the proper time interval between consecutive pulse arrivals at Earth. In linearized general relativity, we derive a general expression for this proper time shift and show that it decomposes into Doppler, Shapiro, and Einstein delay contributions whose sum is gauge invariant, similar to frameworks that have been developed for other gravitational-wave detectors such as laser and atom interferometers. We also provide a recipe for computing the resulting timing residual for any specified perturbation, and we illustrate the method with several physically well-motivated sources, recovering known results where they exist in the literature. This recipe can be directly applied to search for new physics from real pulsar timing data using existing numerical software.