Exact quasinormal modes in Grumiller spacetime

Abstract: 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 $\leq 2$ by introducing a new transformation relation. We find that the quasinormal-mode frequencies are identical for different bosons sharing the same quantum number $N$, and similarly for different fermions. However, the frequencies of bosons and fermions never coincide. Moreover, for a given spin state, the corresponding particles exhibit an $(n + 1)$-fold degeneracy. These results provide a theoretical basis for simulating particle waves with identical statistical properties.