Perturbations of relativistic dissipative stars

Viscous fluids can dissipate and alter the propagation of gravitational waves, as well as modify the relaxation and stability properties of self-gravitating fluids. This is particularly relevant in order to understand the relaxation to equilibrium of neutron stars, and their gravitational wave emission. Here we study the linearized theory of perturbations of spherically symmetric self-gravitating fluids. Dissipative effects are included through the hydrodynamics theory of Bemfica, Disconzi, Noronha, and Kovtun (BDNK). This theory has been shown to be causal and stable, despite involving only first order gradients. We show how the problem reduces to two coupled wave equations in the axial sector, one of them associated to a novel viscous mode, and including explicitly dissipative terms. In the polar sector, we reduce the problem to five coupled wave equations and one additional constraint. We comment on their causal structure, and recover the causality bounds of the BDNK theory.