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

TL;DR

This paper explores the Tolman-Oppenheimer-Volkoff equations for the generalized Chaplygin gas, analyzing standard and phantom cases, and examines how modifications to the equation of state influence the solutions, especially near causality limits.

Contribution

It extends previous work on the TOV equations for the generalized Chaplygin gas by including the phantom case and considering causality-based modifications to the equation of state.

Findings

Superluminal group velocity for α > 1 does not prevent pressure divergence.

Pressure diverges at finite radius in the phantom case.

Modifying the equation of state affects the solutions near the causality limit.

Abstract

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.