Testing dynamical torsion effects on the charged black hole's shadow, deflection angle and greybody with M87* and Sgr. A* from EHT

Poincar\'e Gauge's theory of gravity is the most noteworthy alternative extension of general relativity that has a correspondence between spin and spacetime geometry. In this paper, we use Reissner-Nordstrom-de Sitter and anti-de Sitter solutions, where torsion $\tau$ is added as an independent field, to analyze the weak deflection angles $\hat{\alpha}$ of massive and null particles in finite distance regime. We then apply $\hat{\alpha}$ to determine the Einstein ring formation in M87* and Sgr. A* and determine that relative to Earth's location from these black holes, massive torsion effects can provide considerable deviation, while the cosmological constant's effect remains negligible. Furthermore, we also explore how the torsion parameter affects the shadow radius perceived by both static and co-moving (with cosmic expansion) observers in a Universe dominated by dark energy, matter, and radiation. Our findings indicate that torsion and cosmological constant parameters affect the shadow radius differently between observers in static and co-moving states. We also show how the torsion parameter affects the luminosity of the photonsphere by studying the shadow with infalling accretion. The calculation of the quasinormal modes, greybody bounds, and high-energy absorption cross-section are also affected by the torsion parameter considerably.