The Highly Damped Quasinormal Modes of $d$-dimensional Reissner-Nordstrom Black Holes in the Small Charge Limit

TL;DR

This paper investigates the behavior of highly damped quasinormal modes of higher-dimensional Reissner-Nordström black holes with small charge, confirming previous results and exploring the transition of mode frequencies between charged and uncharged black holes.

Contribution

It provides a detailed analysis of the transition of quasinormal mode frequencies from Reissner-Nordström to Schwarzschild black holes in the high damping limit, including the identification of a critical damping value.

Findings

Confirmed previous results for infinite damping limit.

Calculated the transition of real frequencies between black hole types.

Discovered a critical damping point where the frequency dips to zero.

Abstract

We analyze in detail the highly damped quasinormal modes of $d$-dimensional Reissner-Nordstr$\ddot{\rm{o}}$m black holes with small charge, paying particular attention to the large but finite damping limit in which the Schwarzschild results should be valid. In the infinite damping limit, we confirm using different methods the results obtained previously in the literature for higher dimensional Reissner-Nordstr$\ddot{\rm{o}}$m black holes. Using a combination of analytic and numerical techniques we also calculate the transition of the real part of the quasinormal mode frequency from the Reissner-Nordstr$\ddot{\rm{o}}$m value for very large damping to the Schwarzschild value of $\ln(3) T_{bh}$ for intermediate damping. The real frequency does not interpolate smoothly between the two values. Instead there is a critical value of the damping at which the topology of the Stokes/anti-Stokes lines change, and the real part of the quasinormal mode frequency dips to zero.