  We propose a new probe of the dependence of the fine structure constant,
alpha, on a strong gravitational field using metal lines in the spectra of
white dwarf stars. Comparison of laboratory spectra with far-UV astronomical
spectra from the white dwarf star G191-B2B recorded by the Hubble Space
Telescope Imaging Spectrograph gives limits on the fractional variation of
alpha of (Delta alpha/alpha)=(4.2 +- 1.6)x10^(-5) and (-6.1 +- 5.8)x10^(-5)
from Fe V and Ni V spectra, respectively, at a dimensionless gravitational
potential relative to Earth of (Delta phi) ~ 5x10^(-5). With better
determinations of the laboratory wavelengths of the lines employed these
results could be improved by up to two orders of magnitude.
