Low-mass white dwarfs can either be produced in low-mass X-ray binaries by stable mass transfer to a neutron star , or in a common-envelope phase with a heavier white dwarf companion .
We have searched 8 low-mass white dwarf candidates recently identified in the Sloan Digital Sky Survey for radio pulsations from pulsar companions , using the Green Bank Telescope at 340MHz .
We have found no pulsations down to flux densities of 0.6–0.8 mJy kpc ^ { -2 } and conclude that a given low-mass helium-core white dwarf has a probability of < 0.18 \pm 0.05 of being in a binary with a radio pulsar .