  We employ the La Plata stellar evolution code, LPCODE, to compute the first
set of constant rest-mass carbon-oxygen ultra-massive white dwarf evolutionary
sequences for masses higher than 1.29 Msun that fully take into account the
effects of general relativity on their structural and evolutionary properties.
In addition, we employ the LP-PUL pulsation code to compute adiabatic g-mode
Newtonian pulsations on our fully relativistic equilibrium white dwarf models.
We find that carbon-oxygen white dwarfs more massive than 1.382 Msun become
gravitationally unstable with respect to general relativity effects, being this
limit higher than the 1.369 Msun we found for oxygen-neon white dwarfs. As the
stellar mass approaches the limiting mass value, the stellar radius becomes
substantially smaller compared with the Newtonian models. Also, the
thermo-mechanical and evolutionary properties of the most massive white dwarfs
are strongly affected by general relativity effects. We also provide magnitudes
for our cooling sequences in different passbands. Finally, we explore for the
first time the pulsational properties of relativistic ultra-massive white
dwarfs and find that the period spacings and oscillation kinetic energies are
strongly affected in the case of most massive white dwarfs. We conclude that
the general relativity effects should be taken into account for an accurate
assessment of the structural, evolutionary, and pulsational properties of white
dwarfs with masses above 1.30 Msun.
