Scalar perturbations to naked singularities of perfect fluid

In this paper, we study the instability of naked singularities arising in the Einstein equations coupled with isothermal perfect fluid. We show that the spherically symmetric self-similar naked singularities of this system, are unstable to trapped surface formation, under $C^{1,\alpha }$ perturbations of an external massless scalar field. We viewed this as a toy model in studying the instability of these naked singularities under gravitational perturbations in the original Einstein–Euler system which is non-spherically symmetric.