The search for transiting habitable exoplanets has broadened to include several types of stars that are smaller than the Sun in an attempt to increase the observed transit depth and hence the atmospheric signal of the planet. Of all spectral types, white dwarfs (WDs) are the most favorable for this type of investigation. The fraction of WDs that possess close-in rocky planets is unknown, but several large angle stellar surveys have the photometric precision and cadence to discover at least one if they are common. Ultraviolet observations of WDs may allow for detection of molecular oxygen or ozone in the atmosphere of a terrestrial planet. We use archival Hubble Space Telescope data from the Cosmic Origins Spectrograph to search for transiting rocky planets around UV-bright WDs. In the process, we discovered unusual variability in the pulsating WD GD?133, which shows slow sinusoidal variations in the UV. While we detect no planets around our small sample of targets, we do place stringent limits on the possibility of transiting planets, down to sub-lunar radii. We also point out that non-transiting small planets in thermal equilibrium are detectable around hotter WDs through infrared excesses, and identify two candidates.
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