Some aspects of ModMax (A)dS black holes: Thermodynamics properties, heat engine, shadow, null geodesic and light trajectory

In this paper, we focus on the extraction of electrically charged black holes in the presence of modified Maxwell nonlinear electrodynamics and the cosmological constant, known as ModMax-(A)dS black holes. These black holes are of particular interest due to the substantial influence of the nonlinear Maxwell field (ModMax) and the cosmological constant on their properties. After obtaining exact ModMax-(A)dS black hole solutions, we proceed to study their thermodynamic properties, including conserved and thermodynamic quantities, as well as the first law of thermodynamics in a non-extended phase space. The local and global stabilities of these black holes are then assessed. Local stability is evaluated by examining the heat capacity while determining global stability involves calculating the Helmholtz free energy. Then, we investigate the heat engine of ModMax (A)dS black holes, considering the effects of the ModMax parameter and the cosmological constant on all quantities. Moreover, we explore the imprint of ModMax (A)dS black hole parameters on the critical orbits and shadow radius size, the results are compared with EHT observational data of the Sagittarius A^⁎ black holes. Lastly, the null geodesics and light trajectory are discussed in the presence of the ModMax theory.