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.