We present some of the results of a survey aimed at exploring the asteroseismological potential of the newly-discovered carbon-atmosphere white dwarfs. We show that, in certains regions of parameter space, carbon-atmosphere white dwarfs may drive low-order gravity modes. We demonstrate that our theoretical results are consistent with the recent exciting discovery of luminosity variations in SDSS J1426+5752 and some null results obtained by a team of scientists at McDonald Observatory. We also present follow-up photometric observations carried out by ourselves at the Mount Bigelow 1.6-m telescope using the new Mont4K camera. The results of follow-up spectroscopic observations at the MMT are also briefly reported, including the surprising discovery that SDSS J1426+5752 is not only a pulsating star but that it is also a magnetic white dwarf with a surface field near 1.2 MG. The discovery of $g$-mode pulsations in SDSS J1426+5752 is quite significant in itself as it opens a fourth asteroseismological window, after the GW Vir, V777 Her, and ZZ Ceti families, through which one may study white dwarfs.
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