Effects of non-minimal scalar field couplings with curvature tensors on perturbations in non-commutative Schwarzschild spacetimes

This work presents a comparative analysis of the quasi-normal modes (QNMs) of scalar field perturbations in the non-commutative Schwarzschild black hole spacetime, focusing on two different non-minimal curvature couplings: in the first case the scalar field is coupled to the Ricciscalar while in the second the field's derivatives are coupled to the Einstein tensor. These couplings are important in the cosmological modified gravity models and low energy effects of perturbative quantum gravity. It is shown that though the QNM spectra in two models are approximately the same at low overtone numbers, particularly at fundamental modes, they behave characteristically at higher overtones. Time-domain profiles confirm that while the decay rates are predominantly controlled by the near-horizon physics, the oscillation frequencies distinctly reflect the nature of the curvature couplings. In brief, the kind of scalar-interaction affects the spectral and dynamical characteristics of perturbations especially in the high-frequency regime.