Dynamical Chern-Simons gravity is an extension of general relativity in which the gravitational field is coupled to a scalar field through a parity-violating Chern-Simons term. In this framework, we study perturbations of spherically symmetric black hole spacetimes, assuming that the background scalar field vanishes. Our results suggest that these spacetimes are stable, and small perturbations die away as a ringdown. However, in contrast to standard general relativity, the gravitational waveforms are also driven by the scalar field. Thus, the gravitational oscillation modes of black holes carry imprints of the coupling to the scalar field. This is a smoking gun for Chern-Simons theory and could be tested with gravitational-wave detectors, such as LIGO or LISA. For negative values of the coupling constant, ghosts are known to arise, and we explicitly verify their appearance numerically. Our results are validated using both time evolution and frequency domain methods.

We present a comprehensive study of the massless scalar field perturbation in the Reissner-Nordström anti-de Sitter (RNAdS) space-time and compute its quasinormal modes (QNM). For the lowest lying mode, we confirm and extend the dependence of the QNM frequencies on the black hole charge obtained in previous works. In near extreme limit, under the scalar perturbation we find that the imaginary part of the frequency tends to zero, which is consistent with the previous conjecture based on electromagnetic and axial gravitational perturbations. For the extreme value of the charge, the asymptotic field decay is dominated by a power-law tail, which shows that the extreme black hole can still be stable to scalar perturbations. We also study the higher overtones for the RNAdS black hole and find large variations of QNM frequencies with the overtone number and black hole charge. The nontrivial dependence of frequencies on the angular index $\ell$ is also discussed.

We derive an expression for the quasinormal modes of scalar perturbations in near extreme d-dimensional Schwarzschild–de Sitter and Reissner–Nordström–de Sitter black holes. We show that, in the near extreme limit, the dynamics of the scalar field is characterized by a Pöschl-Teller effective potential. The results are qualitatively independent of the spacetime dimension and field mass.

It is presented a thorough analysis of scalar perturbations in the background of Gauss-Bonnet, Gauss-Bonnet-de Sitter and Gauss-Bonnet-anti-de Sitter black hole spacetimes. The perturbations are considered both in frequency and time domain. The dependence of the scalar field evolution on the values of the cosmological constant $\Lambda$ and the Gauss-Bonnet coupling $\alpha$ is investigated. For Gauss-Bonnet and Gauss-Bonnet-de Sitter black holes, at asymptotically late times either power-law or exponential tails dominate, while for Gauss-Bonnet-anti-de Sitter black hole, the quasinormal modes govern the scalar field decay at all times. The power-law tails at asymptotically late times for odd-dimensional Gauss-Bonnet black holes does not depend on $\alpha$, even though the black hole metric contains $\alpha$ as a new parameter. The corrections to quasinormal spectrum due to Gauss-Bonnet coupling is not small and should not be neglected. For the limit of near extremal value of the (positive) cosmological constant and pure de Sitter and anti-de Sitter modes in Gauss-Bonnet gravity we have found analytical expressions.

We investigate the evolution of a scalar field propagating in Reissner-Nordström anti–de Sitter spacetime. Because of the characteristic of spacetime geometry, the radiative tails associated with a massless scalar field propagation have an oscillatory exponential decay. The object picture of the quasinormal ringing has also been obtained. For small charges, the approach to thermal equilibrium is faster for larger charges. However, after the black-hole charge reaches a critical value, we get the opposite behavior for the imaginary frequencies of the quasinormal modes. Some possible explanations concerning the wiggle of the imaginary frequencies have been given. The picture of the quasinormal modes depending on the multipole index has also been illustrated.

We investigate the late-time behavior of the massive vector field in the background of the Schwarzschild and Schwarzschild–de Sitter black holes. For Schwarzschild black hole, at intermediately late times the massive vector field is represented by three functions with different decay law ${\Psi }_0\sim t^{-(\ell +3/2)}\sin mt$, ${\Psi }_1\sim t^{-(\ell +5/2)}\sin mt$, ${\Psi }_2\sim t^{-(\ell +1/2)}\sin mt$, while at asymptotically late times the decay law $\Psi \sim t^{-5/6}\sin (mt)$ is universal and does not depend on the multipole number $\ell$. Together with a previous study of massive scalar and Dirac fields where the same asymptotically late-time decay law was found, it means that the asymptotically late-time decay law $\sim t^{-5/6}\sin (mt)$ does not depend also on the spin of the field under consideration. For Schwarzschild–de Sitter black holes it is observed in two different regimes in the late-time decay of perturbations: nonoscillatory exponential damping for small values of $m$ and oscillatory quasinormal mode decay for high enough $m$. Numerical and analytical results are found for these quasinormal frequencies.