A relativistic formalism to compute quasi-equilibrium configurations of non-synchronized neutron star binaries

TL;DR

This paper develops a relativistic formalism to model the quasi-equilibrium states of neutron star binaries, including realistic counter-rotating configurations, by deriving a first integral of motion for the fluid velocity field.

Contribution

It introduces a relativistic approach to compute neutron star binary configurations with realistic counter-rotation, extending previous models to more accurate scenarios.

Findings

Derived a first integral of motion for counter-rotating neutron star binaries.

Presented a method to compute velocity fields via solving Poisson equations.

Applicable to both synchronized and counter-rotating binary systems.

Abstract

A general relativistic version of the Euler equation for perfect fluid hydrodynamics is applied to a system of two neutron stars orbiting each other. In the quasi-equilibrium phase of the evolution of this system, a first integral of motion can be derived for certain velocity fields of the neutron star fluid including the (academic) case of co-rotation with respect to the orbital motion (synchronized binaries) and the realistic case of counter-rotation with respect to the orbital motion. The velocity field leading to this latter configuration can be computed by solving three-dimensional vector and scalar Poisson equations.