Perturbations of relativistic dissipative stars

TL;DR

This paper develops a linear perturbation theory for relativistic dissipative stars using the BDNK hydrodynamics framework, revealing new viscous modes and analyzing their causal structure in gravitational wave contexts.

Contribution

It introduces a novel perturbation analysis of dissipative relativistic stars within the BDNK theory, including new viscous modes and causal structure insights.

Findings

Reduction to coupled wave equations in axial and polar sectors

Identification of a new viscous mode in axial perturbations

Analysis of causality bounds in dissipative stellar perturbations

Abstract

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.