Frolov Black Hole Surrounded by Quintessence - II: Quasinormal Modes, Greybody Factors, Deflection Angle and Chaos Bound

In this work, we have examined the scalar quasinormal modes, greybody factors, weak gravitational lensing, and the chaos bound of a Frolov black hole surrounded by a quintessence field. We studied the quasinormal frequencies and deduced that an increase in the value of the quintessence parameter $c$ dissipates the oscillatory behavior and thus slow down the decay of perturbations. The greybody factors are highly dependent on the multipole moment $l$ and BH parameters, with a larger $q$ hindering the transmission and smaller $\alpha_0$ making the barrier steeper. The deflection angle of weak lensing under thin lens approximation, monotonically decreases as the value of impact parameter $b$ increases, and is visibly affected by the parameter $c$, and that $\alpha_0$ and $q$ has very minimal effect. Lastly, we investigated the chaos bound behaviour of photon trajectories in the near-horizon neighbourhood, which indicates that it is satisfied for bigger circular photon orbits but broken for smaller ones, with high-angular-momentum photons being chaotic. This violation of the bound points towards the role of quintessence in modifying the thermodynamic features of the BH, with possible adjustments to the standard Bekenstein-Hawking entropy.