Post-Newtonian Models of Differentially Rotating Neutron Stars

TL;DR

This paper develops a self-consistent method to model differentially rotating neutron stars in the first post-Newtonian approximation, providing insights into their structure and energy ratios during formation.

Contribution

It introduces a novel self-consistent field method for constructing relativistic models of differentially rotating stars at first post-Newtonian order.

Findings

Relativistic models have slightly lower kinetic to gravitational energy ratios than Newtonian models.

The method successfully models nascent neutron stars from white dwarf collapse.

Provides a framework for studying relativistic effects in rotating stellar objects.

Abstract

A self-consistent field method is developed, which can be used to construct models of differentially rotating stars to first post-Newtonian order. The rotation law is specified by the specific angular momentum distribution j(m), where m is the baryonic mass fraction inside the surface of constant specific angular momentum. The method is then used to compute models of the nascent neutron stars resulting from the accretion induced collapse of white dwarfs. The result shows that the ratios of kinetic energy to gravitational binding energy of the relativistic models are slightly smaller than the corresponding values of the Newtonian models.