General relativistic calculations for white dwarfs

The mass-radius relations for white dwarfs are investigated by solving the Newtonian as well as Tolman-Oppenheimer-Volkoff (TOV) equations for hydrostatic equilibrium assuming the electron gas to be non-interacting. We find that the Newtonian limiting mass of 1.4562 M circle dot is modified to 1.4166 M circle dot in the general relativistic case for He-4(2) (and C-12(6)) white dwarfs. Using the same general relativistic treatment, the critical mass for Fe-56(26) white dwarfs is obtained as 1.2230 M circle dot. In addition, departure from the ideal degenerate equation of state (EoS) is accounted for by considering Salpeter's EoS along with the TOV equation, yielding slightly lower values for the critical masses, namely 1.4081 M circle dot for He-4(2), 1.3916 M circle dot for C-12(6) and 1.1565 M circle dot for Fe-56(26) white dwarfs. We also compare the critical densities for gravitational instability with the neutronization threshold densities to find that 42 He and 12 6 C white dwarfs are stable against neutronization with the critical values of 1.4081 M circle dot and 1.3916 M circle dot, respectively. However, the critical masses for O-16(8), Ne-20(10), Mg-24(12), Si-28(14), S-32(16) and Fe-56(26) white dwarfs are lower due to neutronization. Corresponding to their central densities for neutronization thresholds, we obtain their maximum stable masses due to neutronization by solving the TOV equation coupled with the Salpeter EoS.