Exact quasinormal modes in Grumiller spacetime

The Grumiller metric is an effective model for gravity at large distances and plays a significant role in constructing galactic models and explaining dark matter. Here, in Grumiller spacetime, we analytically compute the quasinormal-mode frequencies and wave functions for massless particles with spin [Formula: see text] by introducing a new transformation relation. We find that the quasinormal-mode frequencies are identical for different fermions sharing the same quantum number n. However, no bosonic quasinormal modes associated with Heun polynomials exist. Moreover, for a given frequency [Formula: see text], the corresponding particles exhibit a [Formula: see text]-fold degeneracy. These results provide a theoretical basis for simulating particle waves with identical statistical properties.