Gauge-invariant perturbations of relativistic non-perfect fluids in spherical spacetime

TL;DR

This paper develops a gauge-invariant framework for analyzing non-spherical perturbations of relativistic non-perfect fluids in spherical spacetime, incorporating dissipative effects like viscosity and heat flux, relevant for astrophysical compact objects.

Contribution

It introduces a novel gauge-invariant formalism for perturbations of non-perfect fluids, including dissipative effects, in spherical spacetime, extending previous perfect fluid models.

Findings

Derived wave equations for matter and metric perturbations in polar and axial sectors.

Included dissipative effects such as viscosity and heat flux in the perturbation analysis.

Analyzed the impact of dissipative effects on lower-order multipoles ($l=0,1$).

Abstract

Astrophysical compact objects are usually studied using a perfect fluid model. However, in astrophysical processes out-of-equilibrium, dissipative effects become important to describe the dynamics of the system. In this work, we obtain gauge-invariant non-spherical perturbations of a self-gravitating non-perfect fluid in spherical spacetime. We use the Gerlach-Sengupta formalism to work with gauge-invariant metric perturbations, and the Gundlach-Mart\'in-Garc\'ia approach to transform the equations of tensor perturbations into scalar equations. We calculate the dynamics of the dissipative contributions, e.g., viscosity and heat flux, using the M\"uller-Israel-Stewart equations in the gauge-invariant formalism. We obtain a set of field equations for the evolution of matter and metric perturbations in the polar and axial sectors. Specifically, in the former we find two wave equations sourced by the anisotropic contributions, and the evolution of all matter perturbations for radiative modes ($l\geq 2$). In the axial sector, we find one wave equation coupled to the evolution of matter perturbations. Finally, we comment on the contribution of dissipative effects in the lower-order multipoles ($l=0,1$) for both sectors.