Self-gravitating gaseous spheres in 5D framework

One of the suitable theoretical ideas for the polytrope in the Kaluza-Klein cosmology is discussed. Assuming a 5-dimensional (5D) spacetime model described by the Kaluza-Klein theory of gravity, we implement the energy density and pressure of the polytrope which is a self-gravitating gaseous sphere and still very useful as a crude approximation for more realistic stellar models. Next, we obtain the best-fit values of auxiliary parameters given in the model according to recent observational dataset. Finally, we study some cosmological features and the thermodynamical stability of the model.