Non-comoving description of adiabatic radial perturbations of relativistic stars

TL;DR

This paper introduces a simplified, non-comoving formalism for analyzing adiabatic radial perturbations in relativistic stars, providing analytic solutions and insights into stellar oscillations and stability.

Contribution

It presents a new perturbative approach using a radially static observer frame, simplifying calculations and enabling analytic solutions for various stellar models.

Findings

Derived analytic solutions for stellar perturbations.

Computed oscillation eigenfrequencies for specific models.

Analyzed neutron star stability and damping times.

Abstract

We study adiabatic, radial perturbations of static, self-gravitating perfect fluids within the theory of general relativity employing a new perturbative formalism. We show that by considering a radially static observer, the description of the perturbations can be greatly simplified with respect to the standard comoving treatment. The new perturbation equations can be solved to derive analytic solutions to the problem for a general class of equilibrium solutions. We discuss the thermodynamic description of the fluid under isotropic frame transformations, showing how, in the radially static, non-inertial frame, the stress-energy tensor of the fluid must contain momentum transfer terms. As illustrative examples of the new approach, we study perturbations of equilibrium spacetimes characterized by the Buchdahl I, Heintzmann IIa, Patwardhan-Vaidya IIa, and Tolman VII solutions, computing the first oscillation eigenfrequencies and the associated eigenfunctions. We also analyze the properties of the perturbations of cold neutron stars composed of a perfect fluid verifying the Bethe-Johnson model I equation of state, computing the oscillation eigenfrequencies and the $e$-folding time.