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The detection of gravitational waves resulting from the coalescence of binary black holes by the LIGO-Virgo-Kagra Collaboration has inaugurated a new era in gravitational physics. These gravitational waves provide a unique opportunity to test Einstein’s general relativity and its modifications in the regime of extreme gravity. A significant aspect of such tests involves the study of the ringdown phase of gravitational waves from binary black hole coalescence, which can be decomposed into a superposition of various quasinormal modes. In general relativity, the spectra of quasinormal modes depend on the mass, spin, and charge of the final black hole, but they can also be influenced by additional properties of the black hole spacetime, as well as corrections to the general theory of relativity. In this work, we focus on a specific modified theory known as dynamical Chern-Simons gravity. We employ the modified Teukolsky formalism developed in a previous study and lay down the foundations to investigate perturbations of slowly rotating black holes admitted by the theory. Specifically, we derive the master equations for the ${\mathrm{\Psi }}_0$and ${\mathrm{\Psi }}_4$Weyl scalar perturbations that characterize the radiative part of gravitational perturbations, as well as the master equation for the scalar field perturbations. We employ metric reconstruction techniques to obtain explicit expressions for all relevant quantities. Finally, by leveraging the properties of spin-weighted spheroidal harmonics to eliminate the angular dependence from the evolution equations, we derive two, radial, second-order, ordinary differential equations for ${\mathrm{\Psi }}_0$and ${\mathrm{\Psi }}_4$, respectively. These two equations are coupled to another radial, second-order, ordinary differential equation for the scalar field perturbations. This work is the first attempt to derive a master equation for black holes in dynamical Chern-Simons gravity using curvature perturbations. The master equations we obtain can then be numerically integrated to obtain the quasinormal mode spectrum of slowly rotating black holes in this theory, making progress in the study of ringdown in dynamical Chern-Simons gravity. Published by the American Physical Society2024 

There may exist stellar-mass binary black holes (BBH) which merge while orbiting nearby a supermassive black hole (SMBH). In such a triple system, the SMBH will modulate the gravitational waveform of the BBH through orbital Doppler shift and de Sitter precession of the angular momentum. Future space-based gravitational wave (GW) observatories focused on the milli- and decihertz band will be uniquely poised to observe these waveform modulations, as the GW frequency from stellar-mass BBHs varies slowly in this band while modulation effects accumulate. In this work, we apply the Fisher information matrix formalism to estimate how well space-borne GW detectors can measure properties of BBH+SMBH hierarchical triples using the GW from orbiting BBH. We extend previous work by considering the more realistic case of an eccentric orbit around the SMBH, and notably include the effects of orbital pericenter precession. We find that for detector concepts such as LISA, B-DECIGO, and TianGO, we can extract the SMBH mass and semimajor axis of the orbit with a fractional uncertainty below the 0.1% level over a wide range of triple system parameters. Furthermore, we find that the effects of pericenter precession and orbital eccentricity significantly improve our ability to measure this system. We also find that while LISA could measure these systems, the decihertz detector concepts B-DECIGO and TianGO would enable better sensitivity to the triple’s parameters. 

Sensing a classical signal using a linear quantum device is a pervasive application of quantum-enhanced measurement. The fundamental precision limits of linear waveform estimation, however, are not fully understood. In certain cases, there is an unexplained gap between the known waveform-estimation quantum Cramér-Rao bound and the optimal sensitivity from quadrature measurement of the outgoing mode from the device. We resolve this gap by establishing the fundamental precision limit, the waveform-estimation Holevo Cramér-Rao bound, and how to achieve it using a nonstationary measurement. We apply our results to detuned gravitational-wave interferometry to accelerate the search for postmerger remnants from binary neutron-star mergers. If we have an unequal weighting between estimating the signal’s power and phase, then we propose how to further improve the signal-to-noise ratio by a factor of √2 using this nonstationary measurement.