Hot white dwarf stars are the ideal probe for a relationship between the fine-structure constant and strong gravitational fields, providing us with an opportunity for a direct observational test. We study a sample of hot white dwarf stars, combining far-UV spectroscopic observations, atomic physics, atmospheric modelling, and fundamental physics in the search for variation in the fine structure constant. This variation manifests as shifts in the observed wavelengths of absorption lines, such as quadruply ionized iron (FeV) and quadruply ionized nickel (NiV), when compared to laboratory wavelengths. Berengut et al. (Phys. Rev. Lett. 2013, 111, 010801) demonstrated the validity of such an analysis using high-resolution Space Telescope Imaging Spectrograph (STIS) spectra of G191-B2B. We have made three important improvements by: (a) using three new independent sets of laboratory wavelengths; (b) analysing a sample of objects; and (c) improving the methodology by incorporating robust techniques from previous studies towards quasars (the Many Multiplet method). A successful detection would be the first direct measurement of a gravitational field effect on a bare constant of nature. Here we describe our approach and present preliminary results from nine objects using both FeV and NiV.