Shadow and quasinormal modes of GUP corrected Grumiller black holes

This study investigates the shadows, scalar perturbations, and quasinormal modes (QNMs) of Grumiller black holes (BHs) within the framework of the Generalized Uncertainty Principle (GUP). The GUP introduces quantum corrections that are most significant near the event horizon, while the Rindler acceleration parameter predominantly influences the spacetime at larger distances. We derive analytical expressions for the photon sphere and shadow radii, showing that quantum corrections cause both to decrease. Additionally, we explore the dynamics of massless scalar perturbations and compute the quasinormal frequencies using the higher-order WKB approximation, supported by time-domain analysis. Our results indicate that while the Rindler acceleration significantly impacts the oscillation frequency and damping rate of gravitational wave (GW) ring downs, the effect of the GUP parameters is relatively small. This work clarifies how these distinct influences operate in different regions of the black hole spacetime and provides valuable insights into the quantum-corrected features of black holes, including their shadows and QNMs.