  Ultra-massive H-rich (DA spectral type) white dwarf stars ($M_{\star} > 1.05
M_{\odot}$) are expected to be substantially crystallized by the time they
reach the ZZ Ceti instability strip ($T_{\rm eff} \sim 12\,000$ K).
Crystallization leads to a separation of $^{16}$O and $^{20}$Ne (or $^{12}$C
and $^{16}$O) in the core of ultra-massive WDs, which strongly impacts their
pulsational properties. An additional factor to take into account when modeling
the evolution and pulsations of WDs in this range of masses are the
relativistic effects, which induce changes in the cooling times and the stellar
masses derived from the effective temperature and surface gravity. Given the
arrival of large amounts of photometric data from space missions such as {\it
Kepler}/{\it K2} and {\it TESS}, it is important to assess the impact of
General Relativity in the context of pulsations of ultra-massive ZZ Ceti stars.
In this work, we present results of Newtonian gravity($g$)-mode pulsation
calculations in evolutionary ultra-massive WD models computed in the frame of
the General Relativity theory.
