Quasinormal modes and shadow of Schwarzschild-Tangherlini black hole with GUP

Abstract

In this work, we investigate quasinormal modes and the shadow of a Schwarzschild-Tangherlini black hole in $(d+1)$ dimensions, incorporating corrections arising from the Generalized Uncertainty Principle (GUP). Using the WKB approximation up to sixth order, we calculate the quasinormal frequencies for $l=1, 2$ and $d=3, 4, 5, 6$, and analyze the effects of the dimensionless linear and quadratic GUP parameters $\barα$ and $\barβ$, respectively. We find that the linear correction increases the oscillation frequency and the damping rate, whereas the quadratic correction produces the opposite behavior within the parameter range considered. Using the finite difference scheme, we obtain the time-domain evolution and find that higher dimensions lead to faster damping and that the visibility of GUP-induced modifications to the time-domain waveform depends on the excitation profile of the initial perturbation, whereas the underlying quasinormal spectrum remains determined by the black hole geometry.Furthermore, we investigate the shadow and establish its correspondence with the quasinormal spectrum in the eikonal limit through the properties of the unstable circular null geodesics. Finally, we confront the predicted shadow size with Event Horizon Telescope observations of Sagittarius A* and use these constraints to investigate the allowed GUP parameter space.