Abstract
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.
Highlights
The recent detection of gravitational waves (GWs) from binary black hole (BH) mergers and neutron stars by the LIGO and Virgo Collaborations [1,2,3,4], has provided us with a new window to study and understand physical processes at extreme conditions, where the role of gravity by far dominates the other known forms of interactions in nature
We have found the quasinormal mode (QNM) frequencies of a class of static spherically symmetric spacetimes having a smeared matter distribution, parametrized by Θ, an inherent length scale
II we have briefly reviewed the basic aspects of QNMs and an elementary method to obtain them for static spherically symmetric Schwarzschild spacetime
Summary
The recent detection of gravitational waves (GWs) from binary black hole (BH) mergers and neutron stars by the LIGO and Virgo Collaborations [1,2,3,4], has provided us with a new window to study and understand physical processes at extreme conditions, where the role of gravity by far dominates the other known forms of interactions in nature. For the present work we are assuming that these collapse events are generally consistent with the theoretical predictions of general relativity [5], later works [6] have shown that there are significant deviations These observations firmly suggest studying the possibility of having alternative sources that can account for such deviations in GW characteristic frequencies. The popularly known GWs as observed by the LIGO/ Virgo Collaboration are the quasinormal modes (QNMs) [7,8,9,10] The waveforms of these GW signals consist of three parts: (1) inspiral, (2) merger, and (3) ring down.
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