Phenomenology of Schwarzschild-like black holes with a generalized Compton wavelength

We investigate the influence of the generalized Compton wavelength (GCW), emerging from a three-dimensional dynamical quantum vacuum (3D DQV) on Schwarzschild-like black hole spacetimes. The GCW modifies the classical geometry through a deformation parameter epsilon, encoding quantum gravitational back-reaction. We derive exact analytical expressions for the black hole shadow radius, photon sphere, and weak deflection angle, incorporating higher-order corrections and finite-distance effects of a black hole with generalized Compton effect (BHGCE). Using Event Horizon Telescope (EHT) data, constraints on epsilon are obtained: epsilon is an element of [-2.572, 0.336] for Sgr. A* and epsilon is an element of [-2.070, 0.620] for M87*, both consistent with general relativity yet allowing moderate deviations. Weak lensing analyses via the Keeton-Petters and Gauss-Bonnet formalisms further constrain epsilon approximate to 0.061, aligning with solar system bounds. We compute the modified Hawking temperature, showing that positive epsilon suppresses black hole evaporation. Quasinormal mode frequencies in the eikonal limit are also derived, demonstrating that both the oscillation frequency and damping rate shift under GCW-induced corrections. Additionally, the gravitational redshift and scalar perturbation waveform exhibit deformations sensitive to epsilon. Our results highlight the GCW framework as a phenomenologically viable semiclassical model, offering testable predictions for upcoming gravitational wave and VLBI observations.