Yerçekimsel dalgalar ve 2.5 PN yerçekimsel dalga hafızası

Since the discovery of general relativity, the Einstein field equations have explained many phenamenon (e.g. precession of orbits) and predicted others (e.g. gravitational lensing, gravitational time dilation and black holes). Among its many predictions, the wave-like nature of the linearized theory has garnered a lot of attention due to the possiblity of gravitational wave propagation; their effects, their observability and the complicated nature of gravitational radiation. Many scientists (that can be found in references) have worked on ways to approach the non-linear limit of this theory through methods such as post-Newtonian (PN) expansion and post-Monkowskian ex- pansion. From these methods, one can find that for weakly self-gravitating object, we can approximate the production of waves up to corrections of O(v/c^n). These corrections also predicts observable gravitational corrections in the far zone called "memory effect". This effect corresponds to a permanent change in the metric after the wave has long passed the observer. In this thesis, I will go through the process of deriving these intriguing predictions which are soon to be put to the test by free-fall interferometers (e.g. LISA and DECIGO) or matter-wave interferometers (e.g. MIGA).