Viscoelastic nonradial stellar pulsation framework in general relativity

Neutron stars are typically studied under perfect fluid idealizations, but there are situations where one wants to consider more generic models to study a broader range of astrophysical situations, such as anisotropy due to strong magnetic fields. One robust way to model matter is by introducing viscosity and elasticity to the medium under consideration, and there has been much recent interest and important developments in general relativistic viscoelastic theory. In this work, we incorporate these recent developments to formulate nonradial stellar pulsations by introducing viscoelasticity perturbatively, which provides the first fully relativistic viscoelastic neutron star model. This kind of model can capture some physical aspects of neutron stars, such as superfluidity in the crust and viscosity in the bulk. The model can extend any work where purely viscous/elastic systems are considered, and it provides a consistent framework to study the stability of stars that deviate from ideal fluid models. We shall demonstrate how our model gives a consistent relativistic formulation and leads to sensible thermodynamic relations.