Dirac Quasinormal Modes in Noncommutative Reissner-Nordström Black Holes

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 ($r-\phi$) 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.

12 pages, 4 figures, contribution to the "XLII Workshop on Geometric Methods in Physics" June 30 - July 5, 2025, Białystok, Poland