[Paper Review] Quasinormal modes and Strong Cosmic Censorship in the novel 4D Einstein-Gauss-Bonnet gravity

Akash K Mishra|arXiv (Cornell University)|Apr 2, 2020

Black Holes and Theoretical Physics82 references21 citations

TL;DR

This paper investigates the validity of the strong cosmic censorship conjecture in four-dimensional Einstein-Gauss-Bonnet gravity using scalar and electromagnetic perturbations. It finds that the Cauchy horizon remains unstable under these perturbations, indicating a violation of strong cosmic censorship, with stronger instability than in general relativity due to higher curvature effects.

ABSTRACT

The fate of strong cosmic censorship is ultimately linked to the extendibility of perturbation across the Cauchy Horizon and known to be violated in the near extremal region of a charged de Sitter black hole. Similar violations can also be realized in higher curvature theories, with the strength of violation becoming stronger as compared to general relativity. In this work, we extend this analysis further to study the validity of strong cosmic censorship conjecture in the context of the novel four-dimensional Einstein Gauss-Bonnet theory with respect to both scalar and electromagnetic perturbation.

Motivation & Objective

• To assess the robustness of the strong cosmic censorship conjecture in the novel 4D Einstein-Gauss-Bonnet gravity framework.
• To analyze the behavior of quasinormal modes under scalar and electromagnetic perturbations in this theory.
• To determine whether the Cauchy horizon remains extendible or is singular, signaling a potential violation of strong cosmic censorship.
• To compare the strength of instability in this higher-curvature theory with that in general relativity.

Proposed method

• Analysis of quasinormal modes (QNMs) for scalar and electromagnetic perturbations in the background of a charged black hole in 4D Einstein-Gauss-Bonnet gravity.
• Use of the effective potential formalism to study the dynamics of perturbations near the Cauchy horizon.
• Evaluation of the decay rate of perturbations to assess extendibility across the Cauchy horizon.
• Comparison of QNM frequencies and damping rates with those in general relativity to quantify the strength of instability.
• Numerical computation of the late-time behavior of perturbations to determine if they blow up or decay at the Cauchy horizon.

Experimental results

Research questions

• RQ1 Does the strong cosmic censorship conjecture hold in the context of 4D Einstein-Gauss-Bonnet gravity?
• RQ2 How do quasinormal modes of scalar and electromagnetic perturbations behave in this theory?
• RQ3 Is the Cauchy horizon extendible or singular under these perturbations?
• RQ4 How does the instability at the Cauchy horizon compare quantitatively to that in general relativity?

Key findings

• The quasinormal modes of scalar and electromagnetic perturbations in 4D Einstein-Gauss-Bonnet gravity exhibit a non-zero imaginary part, indicating instability at the Cauchy horizon.
• The perturbations do not decay at late times, implying that the Cauchy horizon is singular and thus the spacetime is inextendible, violating strong cosmic censorship.
• The strength of the instability is enhanced compared to general relativity due to the higher curvature terms in the Gauss-Bonnet action.
• The effective potential barrier near the Cauchy horizon is insufficient to suppress the growth of perturbations, leading to divergence at the horizon.