  About 10% of all stars exhibit absorption lines of ultra-high excited (UHE)
metals (e.g. OVIII) in their optical spectra when entering the white dwarf
cooling sequence. The recent discovery of a both spectroscopic and photometric
variable UHE white dwarf led to the speculation that the UHE lines might be
created in a shock-heated circumstellar magnetosphere. We investigate
(multi-band) light curves from several ground- and space-based surveys of all
16 currently known UHE white dwarfs (including one newly discovered) and eight
white dwarfs that show only the HeII line problem, as both phenomena are
believed to be connected. We find that $75^{+8}_{-13}$% of the UHE white
dwarfs, and $75^{+9}_{-19}$% of the HeII line problem white dwarfs are
significantly photometrically variable, with periods ranging from 0.22d to
2.93d and amplitudes from a few tenth to a few hundredth mag. The high
variability rate is in stark contrast to the variability rate amongst normal
hot white dwarfs (we find $9^{+4}_{-2}$%), marking UHE and HeII line problem
white dwarfs as a new class of variable stars. The period distribution of our
sample agrees with both the orbital period distribution of post-common envelope
binaries and the rotational period distribution of magnetic white dwarfs if we
assume that the objects in our sample will spin-up as a consequence of further
contraction. The lack of increasing photometric amplitudes towards longer
wavelengths, as well as the non-detection of optical emission lines arising
from the highly irradiated face of a hypothetical secondary in the optical
spectra of our stars, makes it seem unlikely that an irradiated late type
companion is the origin of the photometric variability. Instead, we believe
that spots on the surfaces of these stars and/or geometrical effects of
circumstellar material might be responsible. (abridged)
