Proper Time Shifts in Pulsar Timing Arrays
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 su…