Shadow, quasinormal modes and Hawking radiation of ModMax black holes in a quintessence background

The modified Maxwell theory (ModMax) is a nonlinear electrodynamics theory with the same symmetries as Maxwell electrodynamics. According to current findings, dark energy makes up a significant part of the universe. In this study, a static spherically symmetric black hole (BH) is simulated with the quintessence matter field and examine the impact of this dark energy. We investigate the metric features of the BH, followed by the effects of the quintessence field as well as the intrinsic parameter of ModMax theory on shadow cast, quasinormal modes, greybody bounds, and Hawking radiation sparsity. We specifically examined the shadow cast by these black holes and derived analytical solutions for both the radius of the photon sphere and the shadow radius. Our findings show that the presence of quintessence and the ModMax parameter have a positive impact on the radii of photon orbits and shadow radius. We then use the 6th order WKB approximation to analyse the QNMs of the ModMax BH solution’s scalar and electromagnetic field perturbations. The model parameters affect QNM frequencies. We found that, that quintessence causes scalar and electromagnetic field perturbations to oscillate quicker and decay more slowly. After that we study the greybody factor and Hawking radiation sparsity. We show that, the existence of quintessence field has a positive impact on the transmission probability of Hawking radiation and inspection of Hawking’s sparsity reveals particular scenarios depending on the values of ${\omega }_q$.