There is growing interest in using current and future gravitational-wave interferometers to search for anisotropies in the gravitational-wave background. One guaranteed anisotropic signal is the kinematic dipole induced by our peculiar motion with respect to the cosmic rest frame, as measured in other full-sky observables such as the cosmic microwave background. Our prior knowledge of the amplitude and direction of this dipole is not explicitly accounted for in existing searches by LIGO/Virgo/KAGRA, but could provide crucial information to help disentangle the sources which contribute to the gravitational-wave background. Here we develop a targeted search pipeline which uses this prior knowledge to enable unbiased and minimum-variance inference of the dipole magnitude. Our search generalises existing methods to allow for a time-dependent signal model, which captures the annual modulation of the dipole due to the Earth's orbit. We validate our pipeline on mock data, demonstrating that neglecting this time dependence can bias the inferred dipole by as much as O(10%). We then run our analysis on the full LIGO/Virgo O1+O2+O3 dataset, obtaining upper limits on the dipole amplitude that are consistent with existing anisotropic search results.

We develop a novel technique through spectral decompositions to study the gravitational perturbations of a black hole, without needing to decouple the linearized field equations into master equations and separate their radial and angular dependence. We first spectrally decompose the metric perturbation in a Legendre and Chebyshev basis for the angular and radial sectors respectively, using input from the asymptotic behavior of the perturbation at spatial infinity and at the black hole event horizon. This spectral decomposition allows us to then transform the linearized Einstein equations (a coupled set of partial differential equations) into a linear matrix equation. By solving the linear matrix equation for its generalized eigenvalues, we can estimate the complex quasinormal frequencies of the fundamental mode and various overtones of the gravitational perturbations simultaneously and to high accuracy. We apply this technique to perturbations of a non-spinning, Schwarzschild black hole in general relativity and find the complex quasinormal frequencies of 2 fundamental modes and their first 2 overtones. We demonstrate that the technique is robust and accurate, in the Schwarzschild case leading to relative fractional errors of ≤ 10 −10 − 10 −8 for the fundamental modes, ≤ 10 −7 − 10 −6 for their first overtones, ≤ 10 −7 − 10 −4 for their second overtones. This method can be applied to any black hole spacetime, irrespective of its Petrov type, making the numerical technique extremely powerful in the study of black hole ringdown in and outside general relativity.

Solving the problem of dark matter remains one of the greatest unsolved mystery of fundamental physics. One possible dark matter candidate is the scalar ultralight boson, with mass « 1eV. If they exist, ultralight bosons will form clouds of significant total mass about rotating black holes, affecting the spacetime around the black hole. After the inspiral phase of a binary merger, the bosonic cloud can affect the perturbations to the black hole, resulting in deviations in the quasinormal mode frequencies of the ringdown signal of a binary merger. Here, we compute these shifts in the gravitational quasinormal mode frequencies for such a system, and conduct an injection campaign with supermassive black holes detected by the Laser Interferometer Space Antenna. We find that detections of the ringdown phase of supermassive black holes can rule out or confirm the existence of cloud-forming ultralight bosons of mass ∼ 10−18eV at redshift z > 1 if cloud dissipation effects during the inspiral can be neglected.