Black holes surrounded by dark matter spike: Spacetime metrics and gravitational wave ringdown waveforms

Abstract

The supermassive black holes at the centers of galaxies may be surrounded by dark matter spike, which could leave detectable imprints on the gravitational wave signals they emit. In this work, combining the mass model of M87, we present black hole analytical solutions in dark matter spike from the Tolman-Oppenheimer-Volkof equations. Meanwhile, the gravitational waves emitted at the ringdown phase of the black holes under the axial gravitational perturbation is investigated, and compare them with the Schwarzschild black hole. The main research methods are time domain integration method and continued fraction method. Besides, the impact of the different dark matter parameters on the quasinormal frequencies is investigated and its detectability on these impacts based on the space-based detectors. Our results indicate that the impacts of dark matter spike on the quasinormal frequencies of black holes can reach up to the order of $10^{-4}$. These results may provide some help in further exploring the impact of dark matter spike on the black holes and their related gravitational wave phenomena.