More about the Tolman-Oppenheimer-Volkoff equations for the generalized Chaplygin gas

We investigate the Tolman-Oppenheimer-Volkoff equations for the generalized Chaplygin gas with the aim of extending the findings of V. Gorini, U. Moschella, A. Y. Kamenshchik, V. Pasquier, and A. A. Starobinsky [Phys. Rev. D {\bf 78}, 064064 (2008)]. We study both the standard case, where we reproduce some previous results, and the phantom case. In the phantom case we show that even a superluminal group velocity arising for $\alpha > 1$ cannot prevent the divergence of the pressure at a finite radial distance. Finally, we investigate how a modification of the generalized Chaplygin gas equation of state, required by causality arguments at densities very close to $\Lambda$, affects the results found so far.