White-dwarf asteroseismology with the {\sl TESS} space telescope

Abstract: As white-dwarf (WD) stars cool, they go through one or more stages of $g$(gravity)-mode pulsational instability, becoming multiperiodic variable stars. Stars passing through these instability domains allow astronomers to study their interiors through asteroseismological techniques, as if they could "look" at their interiors by analyzing the spectra of pulsation periods. WD asteroseismology has experienced extraordinary advances in recent years thanks to photometric observations of unprecedented quality delivered by space missions such as Kepler and TESS. These advances in the monitoring of variable WDs have been accompanied by the development of new stellar models and techniques for modeling their pulsations. In this article, we review the most outstanding findings -- up to early 2022 -- about these fascinating pulsating stars made possible with the high-sensitivity and continuous observations of the ongoing TESS mission, bearing in mind that there will possibly be many more new results in the immediate future derived from this unique space telescope.