The present study focuses on investigating the deflection angle in the weak-field approximation, shadow, quasinormal modes using Lyapunov exponents, and the lower bound of the greybody factor for a charged Kiselev black hole in Rastall gravity. The weak deflection angles are calculated using the Gauss-Bonnet method. They decrease with increasing impact parameter b and charge Q, but gradually increase with increasing black hole mass m. Notably, the presence of a surrounding Kiselev-type matter field in Rastall gravity leads to a higher deflection angle compared to Schwarzschild or Reissner–Nordström black holes with positive 𝒩 q . The photon sphere and shadow of the black hole are analysed concerning the charge Q and mass m; they shrink as Q increases and expand with increasing m. We further analyse the quasinormal modes of the black hole, explicitly derive the coordinate time Lyapunov exponent λ c and the quasinormal frequency 𝓌. In the eikonal limit, the Lyapunov exponent ensures that the real and imaginary parts of the quasinormal modes can be expressed by the frequency and instability time scale of the unstable null circular geodesics. Additionally, we derive the lower bounds of the greybody factor 𝒈 b , it decreases for increasing charge Q while the increasing mass m enhances it. Importantly, all the findings reduce to those of the Reissner–Nordström black hole for 𝒩 q = 0 and to the Schwarzschild black hole for 𝒩 q = Q = 0.
Sarkar et al. (Thu,) studied this question.