# Even parity potential for spacetimes with Gaussian matter source and its associated QNM spectra

## TL;DR

This paper derives the even mode potential for gravitational perturbations in spherically symmetric spacetimes with Gaussian matter sources and computes associated QNM spectra, revealing deviations from isospectrality at certain smearing scales.

## Contribution

It introduces a general form of the even mode potential for such spacetimes and analyzes how Gaussian matter source parameters affect QNM spectra.

## Key findings

- QNM frequencies are computed numerically using WKB approximation.
- The smearing parameter {b8} influences the isospectrality of modes.
- An upper bound on {b8} is identified where spectra deviate.

## Abstract

We have obtained the general form of even mode potential function for the gravitational perturbation of a static spherically symmetric spacetime. Considering the minimal-spread Gaussian matter source, parameterized by a smearing length scale {\Theta}, the associated quasinormal mode (QNM) frequencies are computed numerically using the well known WKB formula. A comparative study on the accuracy of the results based on different approximation orders of the WKB formula indicates that the smearing parameter {\Theta} has an upper bound, beyond which the spectra of odd and even modes deviate from their usual isospectral nature.