  Variations in the pulsation arrival time of five independent pulsation
frequencies of the DB white dwarf EC 20058-5234 individually imitate the
effects of reflex motion induced by a planet or companion but are inconsistent
when considered in unison. The pulsation frequencies vary periodically in a
12.9 year cycle and undergo secular changes that are inconsistent with simple
neutrino plus photon-cooling models. The magnitude of the periodic and secular
variations increases with the period of the pulsations, possibly hinting that
the corresponding physical mechanism is located near the surface of the star.
The phase of the periodic variations appears coupled to the sign of the secular
variations. The standards for pulsation-timing-based detection of planetary
companions around pulsating white dwarfs, and possibly other variables such as
subdwarf B stars, should be re-evaluated. The physical mechanism responsible
for this surprising result may involve a redistribution of angular momentum or
a magnetic cycle. Additionally, variations in a supposed combination frequency
are shown to match the sum of the variations of the parent frequencies to
remarkable precision, an expected but unprecedented confirmation of theoretical
predictions.
