Neutron star evolution with the Bemfica-Disconzi-Noronha-Kovtun viscous hydrodynamics framework

The recently proposed first-order viscous relativistic hydrodynamics formulation by Bemfica, Disconzi, Noronha, and Kovtun (commonly known as the BDNK formulation) has been shown to be causal, stable, strongly hyperbolic, and thus locally well posed. It is now a viable new option for modeling out-of-equilibrium effects in fluids, and has attracted wide attention in its potential applications to astrophysical systems. In this work, we present the first nonlinear numerical simulation of spherically symmetric neutron stars using the BDNK formulation under the Cowling approximation. Using a simplified equation of state, we show that stable evolutions can be constructed within a restricted parameter space up to the simulation time we explored. From these simulations, we analyze the frequency content of the quasinormal modes and the decay rate of the fundamental mode. This analysis serves as a first step toward constructing a fully consistent model of neutron stars using the BDNK formulation.