Quasinormal modes for the scattering on a naked Reissner-Nordstrom singularity

What should be the quasinormal modes associated with a space-time that contains a naked singularity instead of a black hole? In the present work we address this problem by studying the scattering of scalar fields on a curved background described by a Reissner-Nordstrom space-time with vertical bar q vertical bar > m. We show that there is a qualitative difference between cases with 1 < q(2)/m(2) less than or similar to 9/8 and cases with q(2)/m(2) greater than or similar to 9/8. We discuss the necessary conditions for the well-posedness of the problem and present results for the low damped modes in the low l and large l limit. We also consider the asymptotically highly damped quasinormal modes. We present strong evidence that such modes are absent in the case of a naked Reissner-Nordstrom singularity, corroborating recent conjectures relating them to classical and quantum properties of horizons.