  In this work we investigate the structure of white dwarfs using the
Tolman-Oppenheimer-Volkoff equations and compare our results with those
obtained from Newtonian equations of gravitation in order to put in evidence
the importance of General Relativity (GR) for the structure of such stars. We
consider in this work for the matter inside white dwarfs two equations of
state, frequently found in the literature, namely, the Chandrasekhar and
Salpeter equations of state. We find that using Newtonian equilibrium
equations, the radii of massive white dwarfs ($M>1.3M_{\odot}$) are
overestimated in comparison with GR outcomes. For a mass of $1.415M_{\odot}$
the white dwarf radius predicted by GR is about 33\% smaller than the Newtonian
one. Hence, in this case, for the surface gravity the difference between the
general relativistic and Newtonian outcomes is about 65\%. We depict the
general relativistic mass-radius diagrams as
$M/M_{\odot}=R/(a+bR+cR^2+dR^3+kR^4)$, where $a$, $b$, $c$ and $d$ are
parameters obtained from a fitting procedure of the numerical results and
$k=(2.08\times 10^{-6}R_{\odot})^{-1}$, being $R_{\odot}$ the radius of the Sun
in km. Lastly, we point out that GR plays an important role to determine any
physical quantity that depends, simultaneously, on the mass and radius of
massive white dwarfs.
