We present radial velocity observations of four extremely low-mass ( 0.2 ~ { } M _ { \odot } ) white dwarfs .
All four stars show peak-to-peak radial velocity variations of 540 – 710 km s ^ { -1 } with 1.0 – 5.9 hr periods .
The optical photometry rules out main-sequence companions .
In addition , no milli-second pulsar companions are detected in radio observations .
Thus the invisible companions are most likely white dwarfs .
Two of the systems are the shortest period binary white dwarfs yet discovered .
Due to the loss of angular momentum through gravitational radiation , three of the systems will merge within 500 Myr .
The remaining system will merge within a Hubble time .
The mass functions for three of the systems imply companions more massive than 0.46 ~ { } M _ { \odot } ; thus those are carbon/oxygen core white dwarfs .
The unknown inclination angles prohibit a definitive conclusion about the future of these systems .
However , the chance of a supernova Ia event is only 1 % to 5 % .
These systems are likely to form single R Coronae Borealis stars , providing evidence for a white dwarf + white dwarf merger mechanism for these unusual objects .
One of the systems , SDSS J105353.89+520031.0 has a 70 % chance of having a low-mass white dwarf companion .
This system will probably form a single helium-enriched subdwarf O star .
All four white dwarf systems have unusal mass ratios of \leq 0.2 - 0.8 that may also lead to the formation of AM CVn systems .