  The gravitational potential phi = GM/Rc^2 at the surface of the white dwarf
G191-B2B is 10,000 times stronger than that at the Earth's surface. Numerous
photospheric absorption features are detected, making this a suitable
environment to test theories in which the fundamental constants depend on
gravity. We have measured the fine structure constant, alpha, at the white
dwarf surface, used a newly calibrated Hubble Space Telescope STIS spectrum of
G191-B2B, two new independent sets of laboratory Fe V wavelengths, and new
atomic calculations of the sensitivity parameters that quantify Fe V wavelength
dependency on alpha. The two results obtained are: dalpha/alpha = 6.36 +/-
[0.33(stat) + 1.94(sys)] X 10^{-5} and dalpha/alpha = 4.21 +/- [0.47(stat) +
2.35(sys)] X 10^{-5}. The measurements hint that the fine structure constant
increases slightly in the presence of strong gravitational fields. A
comprehensive search for systematic errors is summarised, including possible
effects from line misidentifications, line blending, stratification of the
white dwarf atmosphere, the quadratic Zeeman effect and electric field effects,
photospheric velocity flows, long-range wavelength distortions in the HST
spectrum, and variations in the relative Fe isotopic abundances. None fully
account for the observed deviation but the systematic uncertainties are heavily
dominated by laboratory wavelength measurement precision.
