Polar gravitational perturbations and quasinormal modes of a loop quantum gravity black hole

In this work, we calculate the polar gravitational quasinormal modes for a quantum corrected black hole model, which arises in the context of loop quantum gravity, known as a self-dual black hole. In this way, we calculate the characteristic frequencies using the Wentzel-Kramers-Brillouin approach, where we can verify a strong dependence with the loop quantum gravity parameters. At the same time, we check that the self-dual black hole is stable under polar gravitational perturbations, and we can also verify that the spectrum of the polar quasinormal modes differs from the axial one [M. B. Cruz, C. A. S. Silva, and F. A. Brito, Eur. Phys. J. C 79, 157 (2019)]. Such a result tells us that isospectrality is broken in the context of self-dual black holes.