Stability, quasinormal modes in a charged black hole in perfect fluid dark matter

Abstract

In this work, we study time-like and null geodesics in a charged black hole background immersed in perfect fluid dark matter (PFDM). Using the condition for circular geodesics, we evaluate the energy and angular momentum in terms of the radius (r 0) of the timelike circular orbits. The existence and finiteness of energy and angular momentum constrain the possible range of PFDM parameter (χ) and r 0. In case of null geodesics, we calculate the radius rp of the unstable circular photon orbits. We then use the Lyapunov exponent to study the stability of the geodesics. Then we analyze the critical exponent useful for determining the possibility of detection of gravitational wave signals. After that, we study the perturbation due to a massless scalar field in such a background and calculate the quasinormal mode (QNM) frequencies and their dependence on χ and black hole charge Q. Also, we compare the obtained QNM frequencies both in the exact case and in the eikonal limit. We also calculate the quality factor of the oscillating system and study its dependence on χ and Q. Finally, we evaluate the black hole shadow radius Rs and graphically observe the effect of χ and Q on it.