[Paper Review] Instability of the Novel 4D Charged Einstein-Gauss-Bonnet Anti de-Sitter Black Hole

Peng Liu, Chao Niu+1 more|arXiv (Cornell University)|May 5, 2020

Black Holes and Theoretical Physics4 citations

TL;DR

This study investigates the instability of 4D charged Einstein-Gauss-Bonnet-AdS black holes via quasinormal modes of charged massless scalar perturbations, revealing that superradiance drives the instability. Increasing the Gauss-Bonnet coupling or black hole charge enhances instability, while larger AdS radius or lower perturbation charge improves stability, with monopole modes being less unstable than higher multipoles.

ABSTRACT

We study the instability of the 4D charged Einstein-Gauss-Bonnet-AdS black holes by exploring the quasinormal modes of a charged massless scalar perturbation. We find that the instability is triggered by superradiance. The black hole becomes more unstable when increasing the Gauss-Bonnet coupling constant or the black hole charge. Meanwhile, increasing the AdS radius will make the black holes more stable. Moreover, we find that the system is more unstable for larger perturbation charge. The modes of multipoles are more stable than that of the monopole.

Motivation & Objective

• To investigate the dynamical stability of novel 4D charged Einstein-Gauss-Bonnet-anti-de Sitter black holes under scalar perturbations.
• To determine the role of superradiance in triggering instability in these black hole solutions.
• To analyze how the Gauss-Bonnet coupling constant, black hole charge, and AdS radius influence the instability growth rate.
• To compare the stability of different multipole modes, particularly focusing on monopole versus higher multipoles.

Proposed method

• Solving the Klein-Gordon equation for a charged massless scalar field in the background of 4D charged Einstein-Gauss-Bonnet-AdS black holes.
• Computing quasinormal modes using numerical methods to extract the complex frequency spectrum, where the imaginary part indicates instability growth rate.
• Analyzing the dependence of the quasinormal mode spectrum on the Gauss-Bonnet coupling constant, black hole charge, AdS radius, and perturbation charge.
• Focusing on the superradiant condition to identify the onset of instability in the mode spectrum.
• Comparing stability across different multipole modes (l = 0 for monopole, l ≥ 1 for higher multipoles) by evaluating the imaginary part of the frequency.

Experimental results

Research questions

• RQ1 Does superradiance trigger instability in 4D charged Einstein-Gauss-Bonnet-AdS black holes?
• RQ2 How does increasing the Gauss-Bonnet coupling constant affect the instability growth rate?
• RQ3 How does the black hole charge influence the stability of the system?
• RQ4 What is the impact of the AdS radius on the stability of these black holes?
• RQ5 How do different multipole modes (monopole vs. higher l) compare in terms of instability?

Key findings

• Superradiance is the primary mechanism responsible for the instability observed in 4D charged Einstein-Gauss-Bonnet-AdS black holes.
• Increasing the Gauss-Bonnet coupling constant leads to a higher growth rate of instability, making the black hole more prone to perturbations.
• Larger black hole charge also enhances the instability, indicating a stronger coupling between charge and instability growth.
• Increasing the AdS radius stabilizes the black hole, reducing the imaginary part of the quasinormal mode frequency.
• Higher perturbation charge results in greater instability, with the growth rate increasing as the charge of the scalar field increases.
• Monopole modes (l = 0) are less unstable than higher multipole modes (l ≥ 1), indicating a dependence of instability on angular momentum quantum number.