On the stability of string-hole gas

Focusing on a string-hole gas within the pre-big bang scenario, we study the stability of its solutions in the phase space. We firstly extend the analysis present in the literature relaxing the ideal-gas properties of the string-hole gas, taking into account a (bulk-)viscosity term. Then we consider the case of a theory described by a complete O(d,d)-invariant action up to all orders in $\alpha^{\prime}$-corrections (the Hohm-Zwiebach action), studying the stability of the string-hole gas solution with or without the introduction of the viscosity term. Furthermore, the bulk viscosity is also considered for two different first order $\alpha^{\prime}$-corrected actions: the Gasperini-Maggiore-Veneziano-action and the Meissner-action. The results obtained show how the viscosity can help to stabilize the string-hole gas solution, obtaining constraints on the equation of state of the gas.