[eng] The first detection of a gravitational wave (GW) signal in 2015 by the Laser Interferometer
Gravitational-Wave Observatory (LIGO) detectors opened a new exciting line of research in astrophysics, which allows us to obtain information about the universe through non-electromagnetic
signals. The current network of ground-based observatories is formed by the two LIGO observatories in the United States (Hanford and Livingstone), one in Italy (Virgo) and one in Japan
(Kagra), which have joined efforts to form the LIGO-Virgo-Kagra (LVK) scientific collaboration.
To date, the LVK has detected about ninety GW events, a number that is expected to increase
significantly in the coming years. Its noise limitations will also improve with the implementation
of new third-generation detectors.
Gravitational lensing is a phenomenon predicted by general relativity (GR) which causes
electromagnetic (EM) and GWs to deflect when passing near a massive object. Although EM
gravitational lensing is widely used in astronomy, GW lensing has not yet been observed. The
type of lensing studied in this work is strong lensing. This effect is caused by massive astronomical objects such as galaxies or galaxy clusters, allowing us to observe the signal as multiple
time-delayed copies of the initial GW, which we refer to as images.
This thesis will analyse the last stage of merging Kerr black holes (BH), where the newly formed
BH settles producing vibrations, known as the ringdown (RD) phase. This phase is very useful
for studying the frequencies of quasi-normal modes and probing GR through GR tests. Combining lensing and RD in third-generation detectors will give us a new view into GR.
The project aims to probe GR through lensed GW RD and compare its advantages against
non-lensed events, in particular, for the third-generation detector network. In this thesis, we
simulated ten years of binary BH (BBH) merger data, including both lensed and unlensed events,
as observed by the third-generation detectors Cosmic Explorer (CE) and Einstein Telescope
(ET). The simulations were performed using the LeR Python package. From here, we were
able to compute the RD signal-to-noise ratio (SNR) of these events and compare both lensed
and unlensed cases. The unlensed scenario presented a 1.06% of RD-dominated events, while
the lensed case presented a 0.73%. These RD-dominant events are significant because of their
association with larger mass systems and allow us to extract meaningful physics.
We conducted individual RD tests to assess the impact of lensing. Comparing a single unlensed
image with multiple lensed images demonstrated an improvement of (1-3) orders of magnitude
when using multiple lensed images. Additionally, when comparing two stacked unlensed images
with a pair of lensed images, the resulting posteriors were tightened by (2-3) orders of magnitude
when lensed.
The final goal of the project was to perform parameter estimation (PE) on both lensed and
unlensed events focusing on 330 higher-order modes (HOMs). We selected 50 events with the
highest SNR and recovered the δf330 and δτ330 modes successfully. The results indicated that
lensing breaks degeneracies in our GW models by a factor of 11.4 and 6.17 respectively.
Lensing is a not yet observed GW effect, however, current expectations promise an exciting
future for these observations. This work in a novel way and for the first time contributes to the
readiness of the tests of GR also accounting for lensing