Neutron Star Radial Perturbations for Causal, Viscous, Relativistic Fluids

Abstract: Which of the multiple models of causal and stable relativistic viscous fluids that have been developed is best suited to describe neutron stars? The modeling of out-of-equilibrium effects in these relativistic, astrophysical objects must be one with care, as simple Newtonian intuition fails to remain causal. Radial stability of neutron stars is one of the primary conditions for the viability of such out-of-equilibrium models. In this paper, we study radial perturbations of neutron stars for the Eckart, the Bemfica-Disconzi-Noronha-Kovtun, and the M\"uller-Israel-Stewart fluid models of relativistic viscous fluids. We find that for small viscosity, the three models have the same stability properties: they are always stable to bulk and shear viscosity, but they can be unstable to heat conductivity if certain thermodynamic conditions are violated. For the latter case, we derive a necessary criterion for stability to heat conductivity that applies to all three fluids. Moreover, we show that the additional degrees of freedom introduced by the Bemfica-Disconzi-Noronha-Kovtun and the M\"uller-Israel-Stewart models force the perturbations to evolve on fast timescales. Specifically, the Bemfica-Disconzi-Noronha-Kovtun model has additional oscillatory perturbations that propagate with the speed of second sound, while the M\"uller-Israel-Stewart model MIS only exhibits decaying behavior on the fast timescale. This work therefore establishes the first formal results and criteria for radial stability of these three out-of-equiblirium fluid models on the non-trivial, relativistic background of neutron stars.