Dirac Quasinormal Modes in Noncommutative Reissner-Nordström Black Holes

TL;DR

This paper investigates Dirac quasinormal modes (QNMs) in a noncommutative (NC) Reissner–Nordström black hole, where an angular twist induces an off-diagonal metric component $r$–$φ$ and modifies fermion dynamics. The NC Dirac equation is formulated via a Drinfeld twist with $θ^{tφ}=a$, leading to a Schrödinger-like radial equation with an effective potential $V$ linear in $a$. Frequencies are extracted using Leaver’s continued fraction method, with Gauss elimination to reduce a six-term recurrence to a three-term form and Nollert tails for stability. The results show Zeeman-like splitting of the QNM spectrum and altered damping rates that depend on $a$, $qQ$, and the azimuthal number $ν$, indicating that QNMs can probe Planck-scale NC effects in black hole spacetimes, within a perturbative linear-in-$a$ regime. Extensions to massive fermions and extremal black holes remain for future work.

Abstract

Noncommutative (NC) geometry provides a novel approach to probe quantum gravity effects in black hole spacetimes. This work explores Dirac quasinormal modes (QNMs) of a deformed Reissner-Nordström black hole, where noncommutativity induces an effective metric with an additional ($ r-\varphi$) component. Employing a semiclassical model equivalent to a NC gauge theory, we investigate the dynamics of massless Dirac fields and calculate their QNM frequencies using the continued fraction method, enhanced by Gauss elimination to address the six-term recurrence relations. Our results demonstrate notable shifts in oscillation frequencies and damping rates relative to the commutative Reissner-Nordström case, exhibiting a distinctive Zeeman-like splitting in the QNM spectrum driven by the NC parameter.

Figures (4)

• Figure 1: QNM splitting for different values of the magnetic quantum number $\nu$. Top panel: $j = 1/2$, $s = 1/2$; Bottom panel: $j = 3/2$, $s = 1/2$.
• Figure 2: Dependence of fermionic QNMs on $qQ$ for $j = 3/2$, $s = 1/2$.
• Figure 3: Dependence of fermionic QNMs ($j = 3/2$, $s = 1/2$) on $qQ$.
• Figure 4: $\omega_R$–$\omega_I$ portrait of QNMs.