Scalar perturbations of spacetime, greybody factors, weak deflection angles and shadows of black holes in Weyl geometric gravity theory

We present a comprehensive theoretical investigation of black holes within the framework of Weyl geometric gravity which is a conformally invariant extension of General Relativity that naturally incorporates scalar and vector fields. Motivated by the growing need to explore gravitational dynamics beyond Einsteins theory particularly in regimes involving dark energy, dark matter, and quantum gravity we analyze a recently proposed Weyl black hole solution and uncover rich physical phenomena that depart significantly from classical expectations. Our study spans scalar perturbation dynamics, Hawking radiation via greybody factors, gravitational lensing in both vacuum and plasma environments, and shadow formation under infalling spherical accretion. We find that the Weyl coupling parameter $\delta$ and the cosmological curvature term $1/l^2$ act as powerful deformation parameters which significantly enhancing the black holes stability, effecting Hawking radiation, and enlarging and distorting shadow images. Using the Gauss–Bonnet theorem and Jacobi metric formalism, we derive novel analytical expressions for the deflection angles of photons and massive particles demonstrating pronounced velocity dependence and curvature-induced amplification of gravitational lensing. Furthermore, our optical modeling reveals that Weyl geometric effects leave distinct imprints on observed intensities and photon rings.