Master's Thesis Defence: Matilde Serôdio Pereira Neto Garcia

The first detection of gravitational waves in 2015 opened the door to gravitational wave physics, which has allowed us to test gravity, astrophysics and cosmology with unprecedented precision. When emitted by a merging binary of compact objects, such as black holes, gravitational waves propagate mostly unaltered through the cosmos. However, if they encounter objects in their path that are massive/compact enough, those will act as cosmic lenses, affecting their properties. Gravitational lensing offers a unique probe of both the large-scale structure of the Universe and the fundamental properties of gravitational wave propagation. Depending on the properties of the wave, the lens, and the overall physical setup, different lensing regimes arise, each leading to distinct phenomenology which require different formalisms and techniques to describe. 

This master’s thesis gives an overview of different lensing regimes and explores some of the least familiar ones. To start, we go over the weak gravity approximation, where all the information regarding how the wave is amplified, as well as time and phase shifted, is encapsulated in a diffraction integral. This integral can be solved in full, analytically, giving us frequency dependent amplification functions. We test these amplification factors for real waveforms and obtain heavy distortions and modulations in the waveform that lead to mismatches of order 03 and amplifications up to order 14 in favorable setups. There is, in parallel, the option of solving this integral for short waves, which yields the creation of discrete images with time delays and relative magnifications, which is rather familiar since it is howelectromagnetic radiation is lensed. In strong gravity, we focus on the case of a non-rotating black hole acting as a lens, and start by going over the geometric optics regime which, similarly to light, consists of tracing the trajectory of a massless particle in Schwarzschild metric. We find that, for simplistic active galactic nuclei disk models, gravitational waves emitted by a stellar mass binary source located on the disk can loop around the black hole or get deflected by angles of order 2 . Onthe other hand, in the wave optics regime, we solve, through the Regge-Wheeler equation, the scattering of the wave off a black hole and are able to obtain frequency dependent amplification factors. These amplification factors have an overall different behavior from the ones obtained under the weak gravity approximation due to the structure of a black hole when compared to, for example, a point mass. We find that, although the physical system yields small orders of magnitude in the amplification functions, the black hole causes visible and measurable distortions in the wavefront, qualitatively different from the ones in weak gravity, such as polarization mixing and absorption. 

There is yet a lot of progress to be done in, for example, studying the effects of the spin of a black hole in the amplification functions and geodesic deviations, and preforming more accurate population studies of binaries in the vicinity of black holes acting as lenses (triple systems, active galactic nuclei disks). There is also much to be done within the setup we analyze in strong gravity, such as considering different physical setups in order to find more prominent lensing signatures, and, for example, applying them to extend current gravitational wave template banks in order to identify these signals in current and future detections.

Supervisor: Associate Professor Jose Maria Ezquiaga