Quasinormal mode of Schwarzschild black hole with geometric correction

We investigated the quasinormal modes (QNMs) for scalar, Dirac and electromagnetic fields of a Schwarzschild black hole with geometric corrections. In addition to the inherent modes of the Schwarzschild black hole, we discovered the existence of purely imaginary modes induced by the geometric corrections, which dominated the behavior of the perturbation when geometric corrections were pretty small. Notably, we found that these purely imaginary modes are prominent, and their imaginary parts are proportional to the correction parameter $ϵ$. We also explored the large-$l$ limit using the WKB approximation for scalar field. This opens up the possibility of observed geometric corrections in the future.