Quasi-normal modes of naked singularities in presence of non-linear scalar fields

2023/07/10 by O. S. Stashko, Stashko, O. S., Oleh Savchuk +3
Physics and Astronomy · #Pulsars and Gravitational Waves Research #Cosmology and Gravitation Theories #Black Holes and Theoretical Physics

paper · pdf · doi:10.48550/arxiv.2307.04295

Abstract

We study linear perturbations against static spherically symmetric background configurations of General Relativity with a real scalar field (SF), which is minimally coupled with gravity; it is non-linear due to the presence of the self-action potential. The background solutions have a naked singularity at the center of the configuration. The focus is on the stability of the background and fundamental frequencies of the quasi-normal modes (QNM) of the axial perturbations in the Regge-Wheeler gauge. The problem is reduced to one hyperbolic master equation with an effective potential W_{\rm eff}, which turns out to be positive for a general non-negative SF potential; this ensures the linear stability with respect to this kind of perturbations. For numerical simulations, the SF potential was chosen in the power-law form V(ϕ)∼ϕ²ⁿ with 2

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