General Relativistic and Newtonian White Dwarfs

TL;DR

This paper compares the properties and stability of rotating white dwarfs under Newtonian gravity and general relativity, revealing differences in maximum mass, rotation period, and stability criteria.

Contribution

It applies Hartle's formalism to analyze rotating white dwarfs with Chandrasekhar's equation of state in both frameworks, highlighting stability differences.

Findings

Maximum rotating mass ~1.534 M_sun (Newtonian) and ~1.516 M_sun (relativistic)

Minimum rotation period ~0.28 seconds

Relativistic WDs can be axisymmetrically unstable, Newtonian WDs are stable

Abstract

The properties of uniformly rotating white dwarfs (RWDs) are analyzed within the framework of Newton's gravity and general relativity. In both cases Hartle's formalism is applied to construct the internal and external solutions to the field equations. The white dwarf (WD) matter is described by the Chandrasekhar equation of state. The region of stability of RWDs is constructed taking into account the mass-shedding limit, inverse $\beta$-decay instability, and the boundary established by the turning points of constant angular momentum $J$ sequences which separates stable from secularly unstable configurations. We found the minimum rotation period $\sim0.28$ s in both cases and maximum rotating masses $\sim1.534 M_{\odot}$ and $\sim1.516 M_{\odot}$ for the Newtonian and general relativistic WDs, respectively. By using the turning point method we show that general relativistic WDs can indeed be axisymmetrically unstable whereas the Newtonian WDs are stable.