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General Relativity and Quantum Cosmology, gr-qc
Abstract:
The detection of gravitational waves resulting by the LIGO-Virgo-Kagra
collaboration has inaugurated a new era in gravitational physics, providing an
opportunity to test general relativity and its modifications in the strong
gravity regime. One such test involves the study of the ringdown phase of
gravitational waves from binary black-hole coalescence, which can be decomposed
into a superposition of 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 be influenced by additional properties of the black hole, as
well as corrections to general relativity. In this work, we employ the modified
Teukolsky formalism developed in a previous study to investigate perturbations
of slowly rotating black holes in a modified theory known as dynamical
Chern-Simons gravity. Specifically, we derive the master equations for the
$\Psi_0$ and $\Psi_4$ Weyl scalar perturbations that characterize the radiative
part of gravitational perturbations, as well as 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 $\Psi_0$ and $\Psi_4$, respectively. These 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 can 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.
