Topics in the frontiers of gravitational-wave research =: 重力波的前沿研究 ; 重力波的前沿研究 ; Topics in the frontiers of gravitational-wave research =: Zhong li bo de qian yan yan jiu ; Zhong li bo de qian yan yan jiu

Ph.D. ; Gravitational waves are the result of cataclysmic events that distort the very fabric of space and time. When a gravitational wave travels, it stretches and squeezes space-time around it, resulting in distance variations. ; An important sub-field of gravitational waves is the gravitational lensing of gravitational waves, detectable in LISA and LIGO/Virgo. Recent studies suggest that lensed gravitational waves could be detected in LIGO as early as in the coming decade. Unlike in lensing of light, where we detects particles, in gravitational-wave lensing, we detect waves. Consequently, methods to detect and utilize gravitational wave lensing are entirely different from that of light. This thesis presents methodologies to detect the waves and mock data tests. We also present realistic LIGO/Virgo searches for lensing effects within the first two LIGO/Virgo observation runs O1 and O2. ; Dark matter is among the most mysterious components of the Universe, as none of the standard model particles fit its properties. There are several on-going efforts to search for this elusive particle, whose discovery could fly us past the standard model. We describe methodologies to use gravitational waves to constrain dark matter particles through detection of ``dark matter spikes,'' which form due to the adiabatic growth of massive black holes in galactic centers. We then focus on a unique particle category called ``ultralight boson,'' which is an extremely light particle. Because the particle is light, it has a tremendously large quantum wavelength, allowing it to exhibit quantum effects on large scales. The particles couple to black holes of sizes similar to the boson Compton wavelength, forming massive clouds around rotating black holes through ``superradiance,'' which spins down the black holes to a characteristic spin predicted by classical theories. We demonstrate, through mock data analysis, that LISA observations of extreme-massratio could detect these clouds and perform a rigorous test that could verify their ...