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 $\leq 2$ by introducing a new transformation relation. Our findings indicate that the quasinormal-mode frequencies are identical for different fermions with the same quantum number $n$. Notably, no bosonic quasinormal modes associated with Heun polynomials were found. Furthermore, for a given quasinormal-mode frequency, the corresponding particles exhibit a $2(n + 1)$-fold degeneracy. These results provide a theoretical basis for the mutual simulation of fermionic waves.