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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.

The detection of low-frequency gravitational waves on Earth requires the reduction of displacement noise, which dominates the low-frequency band. One method to cancel test mass displacement noise is a neutron displacement-noise-free interferometer (DFI). This paper proposes a new neutron DFI configuration, a Sagnac-type neutron DFI, which uses a Sagnac interferometer in place of the Mach–Zehnder interferometer. We demonstrate that a sensitivity of the Sagnac-type neutron DFI is higher than that of a conventional neutron DFI with the same interferometer scale. This configuration is particularly significant for neutron DFIs with limited space for construction and limited flux from available neutron sources.