General Relativistic Calculations for White Dwarf Stars

Understand

The mass-radius relations for white dwarf stars 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 $1.4562M_\odot$ is modified to $1.4166M_\odot$ in the general relativistic case for $^4_2$He (and $^{12}_{\ 6}$C) white dwarf stars.
• Using the same general relativistic treatment, the critical mass for $^{56}_{26}$Fe white dwarf is obtained as $1.2230M_\odot$.
• In addition, departure from the ideal degenerate equation of state (EoS) is accounted for by considering Salpeter's EoS along with the TOV equations yielding slightly lower values for the critical masses, namely $1.4081M_{\odot}$ for $^4_2$He, $1.3916M_{\odot}$ for $^{12}_{\ 6}$C and $1.1565M_{\odot}$ for $^{56}_{26}$Fe white dwarfs.