Naked singularity in 4D Einstein-Gauss-Bonnet novel gravity: Echoes and (in)-stability

TL;DR

This paper investigates the stability of a naked singularity in four-dimensional Einstein-Gauss-Bonnet gravity by analyzing perturbations, revealing echoes in the response and conditions under which the spacetime remains stable or becomes unstable.

Contribution

It provides a numerical analysis of perturbations in 4D EGB naked singularity spacetime, highlighting echo phenomena and stability constraints related to the coupling parameter.

Findings

Echoes observed in perturbation profiles for specific modes.

Stability depends on the coupling constant and multipole number.

Higher multipole modes lead to instability, limiting parameter space.

Abstract

We study the stability of an asymptotically flat, static, spherically symmetric naked singularity spacetime in the novel four dimensional Einstein-Gauss-Bonnet (EGB) gravity. The four dimensional EGB black hole for large enough values of the coupling parameter leads to such a naked singularity. The stability and the response of the spacetime is studied against the perturbations by test scalar, electromagnetic and Dirac fields and the time evolution of these perturbations were observed numerically. Implementing a null Dirichlet boundary condition near the singularity, we observed that for l=1 modes of scalar, electromagnetic perturbation and l=0,1 modes of Dirac perturbation the time-domain profile give rise to distinct echoes. However, as the coupling constant is increased, the echoes align and the QNM structure of the 4D-EGB naked singularity-spacetime becomes prominent. For higher values of the multipole number, the spacetime becomes unstable, thereby restricting the parameter space for the coupling parameter.