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

Understand

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.