Exact quasinormal modes in Grumiller spacetime

TL;DR

The paper analyzes quasinormal modes in Grumiller spacetime, a model for gravity at large distances, by unifying massless spin equations into a single radial framework. A new transformation maps the radial part to a Heun equation, and QNM boundary conditions force truncation to Heun polynomials, yielding fermionic frequencies $\omega = -i \kappa_b (n+1)$, independent of spin state and extrinsic angular momentum. No bosonic QNMs associated with Heun polynomials exist in this spacetime. The radial problem reduces to a tridiagonal eigenvalue problem with eigenvalues $Q_{n,m}$, producing a $2(n+1)$-fold degeneracy for each fermionic frequency. This analytic structure enables mutual simulation of fermionic waves and offers a route to infer black-hole parameters from damping factors in Grumiller-like spacetimes, with implications for galactic/dark-matter modeling.

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. 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.