Asymptotic quasinormal frequencies of different spin fields in $d$-dimensional spherically-symmetric black holes

TL;DR

This paper uses the monodromy technique to analyze asymptotic quasinormal frequencies of various spin fields in higher-dimensional black holes, providing new results especially for half-integer spins and exploring their implications for black hole physics.

Contribution

It extends the analysis of aQNFs to half-integer spins in higher-dimensional black holes and validates existing expressions using the monodromy technique.

Findings

Spin-1/2 aQNFs are purely imaginary in most cases.

Spin-3/2 aQNFs resemble spin-1/2 in some black holes but match gravitational perturbations in others.

For certain black holes, the real part of frequencies is fixed while the imaginary part can grow unbounded.

Abstract

While Hod's conjecture is demonstrably restrictive, the link he observed between black hole (BH) area quantisation and the large overtone ($n$) limit of quasinormal frequencies (QNFs) motivated intense scrutiny of the regime, from which an improved understanding of asymptotic quasinormal frequencies (aQNFs) emerged. A further outcome was the development of the "monodromy technique", which exploits an anti-Stokes line analysis to extract physical solutions from the complex plane. Here, we use the monodromy technique to validate extant aQNF expressions for perturbations of integer spin, and provide new results for the aQNFs of half-integer spins within higher-dimensional Schwarzschild, Reissner-Nordstr\"om, and Schwarzschild (anti-)de Sitter BH spacetimes. Bar the Schwarzschild anti-de Sitter case, the spin-1/2 aQNFs are purely imaginary; the spin-3/2 aQNFs resemble spin-1/2 aQNFs in Schwarzschild and Schwarzschild de Sitter BHs, but match the gravitational perturbations for most others. Particularly for Schwarzschild, extremal Reissner-Nordstr\"om, and several Schwarzschild de Sitter cases, the application of $n \rightarrow \infty$ generally fixes $\mathbb{R}e \{ \omega \}$ and allows for the unbounded growth of $\mathbb{I}m \{ \omega \}$ in fixed quantities.