Radial adiabatic perturbations of stellar compact objects

TL;DR

This paper develops a covariant, gauge-invariant framework for analyzing radial adiabatic perturbations in self-gravitating fluids within general relativity, comparing different thermodynamic theories and proposing a stability bound.

Contribution

It introduces a general set of equations applicable to various thermodynamic models and proposes an upper bound on stellar compactness considering causality and pressure anisotropy.

Findings

Compared predictions of Eckart, BDNK, and Israel-Stewart theories on stellar perturbations.

Derived a new solution to Einstein's equations for compact stars.

Proposed an upper bound on maximum stable stellar compactness.

Abstract

We present a covariant and gauge-invariant formulation of the theory of radial adiabatic linear perturbations of self-gravitating, non-dissipative imperfect fluids within the theory of general relativity. By codifying the thermodynamical properties of the source into an equation of state and an ansatz on anisotropic pressure that involves both matter and kinematic variables, we obtain a set of equations that is directly applicable to a wide variety of thermodynamic theories for matter fields. As examples, we evaluate and compare the predictions of the Eckart theory, the Bemfica-Disconzi-Noronha-Kovtun theory, and the Truncated Israel-Stewart theory on the properties and evolution of radial adiabatic perturbations of stellar compact objects modeled by classical equilibrium solutions. Introducing a new solution of the Einstein field equations, and imposing causality, we propose an upper bound for the maximum compactness of dynamically stable stars with non-trivial radial and tangential pressures.