Strong gravitational lensing, quasi-periodic oscillations and constraints from EHT observations for quantum-improved charged black hole

We investigate strong gravitational lensing by quantum-improved charged black holes characterized by an additional parameter denoted as ω ω , in addition to the mass M and charge Q . Our findings reveal that when both the parameters Q /2 M and ω /4M² ω / 4 M 2 increase simultaneously, various astrophysical consequences, such as the deflection angle α D(u) α D ( u ) and angular image separation increase. Concurrently, the angular position θ ∞ θ ∞ , relative magnification rmag r mag , and the time delay Δ T2,1 Δ T 2 , 1 between the first and second relativistic images also decrease with the growing values of the parameters Q /2 M and ω /4M² ω / 4 M 2 . It is also observed that the Einstein ring θ ₁E θ 1 E for the quantum-improved charged black hole is more significant than those for Schwarzschild, quantum-improved Schwarzschild, and Reisner–Nordström black holes. As with supermassive black holes such as M87^* M 87 ∗ and SgrA^* S g r A ∗ , it is observed that to be a viable astrophysical black hole, the EHT results constrain the parameter space ( ω /4M² ω / 4 M 2 , Q /2 M ). Remarkably, the EHT results for SgrA^* S g r A ∗ impose more stringent limits on the parameter space of quantum-improved charged black holes compared to those established by the EHT results for M87^* M 87 ∗ . We investigate the radial profiles of orbital and radial harmonic oscillation frequencies as a function of the dimensionless coupling constants and black hole mass. The main characteristics of test particle quasi-periodic oscillations close to stable circular orbits in the black hole equatorial plane are also examined. We study the positioning of resonant radii in the background of quantum-improved charged black holes for high-frequency quasi-periodic oscillations models: warped disc (WD) models, relativistic precession (RP) and its types, and epicyclic resonance (ER) and its variants.