Quasinormal mode spectra for odd parity perturbations in spacetimes with smeared matter sources

We have found the Quasi Normal Mode (QNM) frequencies of a class of static spherically symmetric spacetimes having a {\it {smeared}} matter distribution, parameterized by $\Theta$ - an inherent length scale. Here our main focus is on the QNMs for the odd parity perturbation in this background geometry. The results presented here for diffused mass distribution reveal significant changes in the QNM spectrum. This could be relevant for future generation (cosmological) observations, specifically to distinguish the signals of GW from a non-singular source in contrast to a singular geometry. We also provide numerical estimates for the $\Theta$-corrected QNM spectrum applicable to typical globular cluster like spherical galaxies having a Gaussian spread in their mass distribution. We find that the $\Theta$-correction to the GW signal due to smeared distribution is accessible to present day observational precision.