Newtonian pulsations of relativistic ONe-core ultra-massive DA white dwarfs

Ultra-massive H-rich (DA spectral type) white dwarf stars ($M_{\star }>1.05M_{\odot }$) are expected to be substantially crystallized by the time they reach the ZZ Ceti instability strip ($T_{\mathrm{e}\mathrm{f}\mathrm{f}}\sim 12000$ 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.