Axial perturbations of Wyman's solution

Wyman's solution is the most general solution to the static spherically-symmetric Einstein massless scalar field equations. It is shown that it has no axial perturbation in which the scalar field is incremented, except in the case where the initial scalar field and the cross-metric increments are negligible. The one dimensional Schrödinger equation which governs axial metrix perturbations is produced.