The Memory Effect of Gravitational Waves in General Relativity: Theoretical overview and observational perspectives

The aim of this thesis is to carry out the study of the memory effect of gravitational waves (GWs). The first chapter is a brief introduction to General Relativity (GR), gravitational waves and their detection. The second chapter is dedicated to a theoretical description of the memory, with its analytical form and its possible sources. Both the linear and the non-linear effects are described, along with their differences in sources and physical interpretations. I will show how these two different effects appear to be the same when considering GWs as massless gravitons. I will also show how to compute the memory for a black holes (BHs) merging. The last chapter deals with perspectives on the memory detection: an analysis of its detectability and its signal to noise ratio (SNR) with the aLIGO and aVIRGO detectors. I will also give an analytical form for the aVIRGO noise expected for the O3 run. Eventually, I will focus on detection via summation of multiple memories and the orphan memory, a memory detected without parent GW signal.