The study of space-time variations of dimensionless physical constants is a necessary approach to search for mysterious phenomena beyond the Standard Model (SM) and General Relativity (GR) motivated by Grand Unification Theories (GUTs). Potentially, the variations of these constants at any location and region of the universe could be tested by using white dwarf spectra with high gravitational fields. Based on the white dwarf star spectra of G191-B2B, our study yields an estimate for the possible cosmological deviations of the proton-to-electron mass ratio, Δμ/μ=(−0.360±0.864)×10−8 with a gravitational redshift z=Δϕ≈5×10−5. This limit serves as an essential tool for examining the framework of the GUTs.