Phenomenology of Schwarzschild-like Black Holes with a Generalized Compton Wavelength

Abstract

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, motivated by the work of Fiscaletti [10.1134/S0040577925020096] \cite{Fiscaletti:2025iuh}. The GCW modifies the classical geometry through a deformation parameter $\epsilon$, encoding quantum gravitational backreaction. 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: $\epsilon \in [-2.572,0.336]$ for Sgr. A* and $\epsilon \in [-2.070,0.620]$ for M87*, both consistent with general relativity yet allowing moderate deviations. Weak lensing analyses via the Keeton-Petters and Gauss-Bonnet formalisms further constrain $\epsilon \approx 0.061$, 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.

14 pages, 3 figures

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