The importance of GR for the radius of massive white dwarfs

In this work we investigate the structure of WD stars using the Tolman-Oppenheimer-Volkoff equations and compare with the Newtonian equations of gravitation in order to put in evidence the importance of the General Relativity in the study of these stars. Instead of using politropic equations of state we have solved the equations using the exact relativistic energy equation for the model of completely degenerate electron gas. We find a good fit of the TOV solution with the general EoS for the WD mass-radius diagram. We propose that our fit has to be used as relation between mass and radius for general relativistic WD instead of that Newtonian M ∼ 1/R³, this fit is given by M = R/(a + bR + cR² + dR³ + kR⁴), where a, b, c and d are parameters and 1/k is the constant of the Newtonian mass-radius relation and it can be used in simulation study of binary systems that occurs accretion