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 are studied against the perturbations by test scalar, electromagnetic and Dirac fields, and the time evolution of these perturbations was 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 profiles give rise to distinct echoes. However, as the coupling constant increases, the echoes align, and the quasinormal mode 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.
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