Even Parity Perturbations of the Janis-Newman-Winicour Singularity

Abstract

In this paper we build upon previous works on odd-parity perturbations to the Janis-Newman-Winicour singularity by extending the analysis to even-parity perturbations. Perturbations to the metric can be decomposed using tensor spherical harmonics and Fourier decomposition, and are further reduced by gauge transformations. By calculating the Einstein field equations and the divergence of the stress-energy tensor, one obtains 8 independent radial equations for the first-order metric perturbations and scalar field perturbation. Through a suitable functional transformation, one can determine a coupled wave equation between a perturbing function and the scalar field, which is most naturally solved using numerical integration techniques. Following this analysis, we briefly discuss the notion of boundary conditions for a globally naked singularity which are essential to proposing a well-defined perturbation problem.