Pseudo-Newtonian Models for the Equilibrium Structures of Rotating Relativistic Stars

TL;DR

This paper introduces a simplified model for rotating relativistic stars that incorporates relativistic effects into a Newtonian framework, providing results closely aligned with full general relativity at reduced computational cost.

Contribution

It presents a novel pseudo-Newtonian approach using active mass density to model equilibrium structures of rotating relativistic stars, bridging the gap between Newtonian and relativistic methods.

Findings

Solutions agree within 5% of general relativistic results

Method is computationally less intensive than full relativistic models

Applicable to neutron stars with relativistic motions or equations of state

Abstract

We obtain equilibrium solutions for rotating compact stars including the special relativistic effects. The gravity is assumed to be Newtonian, but we used the active mass density, which takes into account all the energies such as motions of the fluids, internal energy, pressure energy in addition to the rest mass energy, in computing the gravitational potential using Poisson's equation. Such a treatment could be applicable to the neutron stars with relativistic motions or relativistic equation of state. We applied the Hachisu's self-consistent field (SCF) method to find spheroidal as well as toroidal sequences of equilibrium solutions. Our solutions show better agreement than Newtonian relativistic hydrodynamic approach that does not take into account the active mass, with general relativistic solutions. The physical quantities such as the peak density, equatorial radii of our solutions agree with general relativistic ones within 5%.Therefore our approach can be a simple alternative to the fully relativistic one when large number of model calculations are necessary as it requires much less computational resources.