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 (EE) and angular momentum (LL) in terms of the radius (rcr_c) of the circular orbits. The existence and finite-ness of EE and LL constrain the possible range of PFDM parameter (χ\chi) and the radius of the circular orbit (rcr_c). We then use the Lyapunov exponent (λ\lambda) to study the stability of the geodesics. Then we analyze the critical exponent (γ\gamma) 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 quasinrmal mode (QNM) frequencies and their dependence on PFDM parameter χ\chi and black hole charge QQ. 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\chi and QQ. Finally, we evaluate the black hole shadow radius RsR_s and graphically observe the effect of χ\chi and QQ on it.Comment: 29 pages, 18 Figures; Comments are welcom

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