Irrotational Binary Neutron Stars in Quasiequilibrium in General Relativity

TL;DR

This paper demonstrates that the complex problem of modeling irrotational binary neutron stars in general relativity can be simplified to a more manageable set of equations, facilitating better understanding of their equilibrium states.

Contribution

It extends the Newtonian simplification of irrotational binary neutron star models to general relativity, making the equations easier to solve.

Findings

Simplified equations analogous to Newtonian case derived for general relativity

The new formulation reduces computational complexity

Facilitates the study of binary neutron star equilibrium states

Abstract

Neutron stars in binary orbit emit gravitational waves and spiral slowly together. During this inspiral, they are expected to have very little vorticity. It is in fact a good approximation to treat the system as having zero vorticity, i.e., as irrotational. Because the orbital period is much shorter than the radiation reaction time scale, it is also an excellent approximation to treat the system as evolving through a sequence of equilibrium states, in each of which the gravitational radiation is neglected. In Newtonian gravity, one can simplify the hydrodynamic equations considerably for an equilibrium irrotational binary by introducing a velocity potential. The equations reduce to a Poisson-like equation for the potential, and a Bernoulli-type integral for the density. We show that a similar simplification can be carried out in general relativity. The resulting equations are much easier to solve than other formulations of the problem.