Testing General Relativity and Probing Nuclear Physics in the era of Gravitational Waves
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The LIGO and Virgo detectors have detected 90 gravitational wave events so far. The gravitational waves have come from pairs of black holes or neutron stars. The astrophysical interpretation of these events was made possible by sophisticated modeling of both source and detector noise. In this thesis, I develop and apply model-independent methods to check for biases due to un-modeled astrophysical or terrestrial effects and to search for signals from the remnant of binary neutron star coalescences. The methods use a sine-Gaussian wavelet basis set to reconstruct the gravitational waveform which is sensitive to a wide range of waveform morphologies and enables us to increase detection confidence and improve data quality. I report the results of applying these methods to the first three observing runs of LIGO and Virgo. I also characterize these methods using various simulation studies.