The properties of uniformly rotating white dwarfs ( RWDs ) are analyzed within the framework of general relativity .
Hartle ’ s formalism is applied to construct the internal and external solutions to the Einstein equations .
The WD matter is described by the relativistic Feynman-Metropolis-Teller equation of state which generalizes the Salpeter ’ s one by taking into account the finite size of the nuclei , the Coulomb interactions as well as electroweak equilibrium in a self-consistent relativistic fashion .
The mass M , radius R , angular momentum J , eccentricity \epsilon , and quadrupole moment Q of RWDs are calculated as a function of the central density \rho _ { c } and rotation angular velocity \Omega .
We construct the region of stability of RWDs ( J - M plane ) taking into account the mass-shedding limit , inverse \beta -decay instability , and the boundary established by the turning-points of constant J sequences which separates stable from secularly unstable configurations .
We found the minimum rotation periods \sim 0.3 , 0.5 , 0.7 and 2.2 seconds and maximum masses \sim 1.500 , 1.474 , 1.467 , 1.202 M _ { \odot } for ^ { 4 } He , ^ { 12 } C , ^ { 16 } O , and ^ { 56 } Fe WDs respectively .
By using the turning-point method we found that RWDs can indeed be axisymmetrically unstable and we give the range of WD parameters where it occurs .
We also construct constant rest-mass evolution tracks of RWDs at fixed chemical composition and show that , by loosing angular momentum , sub-Chandrasekhar RWDs ( mass smaller than maximum static one ) can experience both spin-up and spin-down epochs depending on their initial mass and rotation period while , super-Chandrasekhar RWDs ( mass larger than maximum static one ) , only spin-up .