Effect of rainbow function on radial oscillations and some other properties of Chaplygin dark star

In the present article, we have imagined a hypothetical spherically symmetric stellar structure, made by an isotropic fluid satisfying dark energy equation of sate (EOS), named as dark energy star (DES), in the context of gravity’s rainbow. We adopted modified Chaplygin gas EOS with an extra parameter \(\alpha \) satisfying \(0\le \alpha \le 1\). In a recent literature Tudeshki et al. (Phys. Lett. B 848 (2024) 138333) investigated the same type stellar configuration, including the mass-radius relation for \(\alpha =1\). However, we have investigated the effect of the rainbow function on such hypothetical DESs corresponding to \(\alpha =0.8~\text {and}~0.9\). Mainly, we have concentrated on two features like, mass-radius relation and radial oscillations in the effect of rainbow function. After computing the values of maximum mass and corresponding radius of the star, we compared our results with GR and some chosen observed relativistic stellar candidates. Moreover, we have computed the frequencies and shown the behavior of corresponding Eigenfunctions for the six lowest excited modes in the variation of the rainbow function. As a final result, we have our proposed stellar structure is physically reasonable and may be placed in the ‘mass-gap’ region corresponding to some fixed values of model parameters.