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arXiv · 2306.00646

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

Anish Das·Anirban Roy Chowdhury·Sunandan Gangopadhyay
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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 ($E$) and angular momentum ($L$) in terms of the radius ($r_c$) of the circular orbits. The existence and finite-ness of $E$ and $L$ constrain the possible range of PFDM parameter ($\chi$) and the radius of the circular orbit ($r_c$). We then use the Lyapunov exponent ($\lambda$) to study the stability of the geodesics. Then we analyze the critical exponent ($\gamma$) 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 $\chi$ 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 $\chi$ and $Q$. Finally, we evaluate the black hole shadow radius $R_s$ and graphically observe the effect of $\chi$ and $Q$ on it.

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Anish Das, Anirban Roy Chowdhury, Sunandan Gangopadhyay. 2023-06-01. Stability, quasinormal modes in a charged black hole in perfect fluid dark matter. https://arxiv.org/abs/2306.00646

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