Neutron stars in $f(R,T)$ gravity with conserved energy-momentum tensor: Hydrostatic equilibrium and asteroseismology

TL;DR

This paper explores the structure and stability of neutron stars within a modified gravity framework, deriving new equations and analyzing how these stars' properties and oscillations are affected by the $f(R,T)$ gravity model.

Contribution

It introduces a specific $f(R,T)$ gravity model with conserved energy-momentum tensor, deriving modified stellar and pulsation equations for neutron stars.

Findings

Neutron star properties are significantly affected by the $f(R,T)$ gravity modifications.

A cusp indicating instability appears at the minimum of the binding energy.

The fundamental oscillation mode frequency passes through zero at the instability point.

Abstract

We investigate the equilibrium and radial stability of spherically symmetric relativistic stars, considering a polytropic equation of state (EoS), within the framework of $f(R,T)$ gravity with a conservative energy-momentum tensor. Both modified stellar structure equations and Chandrasekhar's pulsation equations are derived for the $f(R,T)= R+ h(T)$ gravity model, where the function $h(T)$ assumes a specific form in order to safeguard the conservation equation for the energy-momentum tensor. The neutron star properties, such as radius, mass, binding energy and oscillation spectrum are studied in detail. Our results show that a cusp -- which signals the appearance of instability -- is formed when the binding energy is plotted as a function of the compact star proper mass. We find that the squared frequency of the fundamental vibration mode passes through zero at the central-density value corresponding to such a cusp where the binding energy is a minimum.