Low-state spectrophotometry of the short-period polar EF Eridani ( P _ { orb } = 81 min ) found the system at V = 18.0 with no trace of the companion ( Wheatley and Ramsay 1998 ) .
We show that the lack of such spectral features implies that the companion to the white dwarf in EF Eri has a spectral type later than M9 and is either a transition object at the brink of hydrogen burning or a brown dwarf .
The optical low state spectrum indicates a temperature of the white dwarf of T _ { eff } = 9500 \pm 500 K. This is one of the coldest white dwarfs in cataclysmic variables , implying a cooling age t _ { cool } \ga 10 ^ { 9 } yrs or accretional heating at a rate as given by gravitational radiation .
The large age of the system excludes a warm brown dwarf as companion .
EF Eri has either just passed through the period minimum of cataclysmic variable stars or has started mass transfer from an old brown dwarf secondary .