A Study of Low Frequency Gravitational Waves

This thesis explores the theoretical framework and observational signatures of low frequency gravitational waves (GWs), in particular, those emitted by supermassive black hole binaries (SMBHBs). Utilizing the framework of general relativity, we examine how GWs perturb spacetime and affect pulsar timing observations. A significant focus is placed on the Hellings-Downs curve, the ”smoking gun” for the detection of the gravitational wave background (GWB), characterizing the expected correlation in timing residuals between pairs of pulsars, using Pulsar Timing Arrays (PTAs). Through detailed analytical derivations and statistical analysis, we show how the Hellings-Downs function emerges from the geometry of GW propagation and the position of pulsar pairs in the sky. Furthermore, we discuss the stochastic GWB produced by an ensemble of SMBHBs and its observational implications, as well as the population of SMBHBs behind such signals. The work synthesizes the mathematical and cosmological principles needed to interpret recent findings by PTA collaborations, such as the North American Nanohertz Observatory for Gravitational waves (NANOGrav).