Spectra of molecular hydrogen (${\mathrm{H}}_2$) are employed to search for a possible proton-to-electron mass ratio ($\mu$) dependence on gravity. The Lyman transitions of ${\mathrm{H}}_2$, observed with the Hubble Space Telescope towards white dwarf stars that underwent a gravitational collapse, are compared to accurate laboratory spectra taking into account the high temperature conditions ($T\sim 13000\mathrm{K}$) of their photospheres. We derive sensitivity coefficients $K_i$ which define how the individual ${\mathrm{H}}_2$ transitions shift due to $\mu$ dependence. The spectrum of white dwarf star GD133 yields a $\mathrm{\Delta }\mu /\mu$ constraint of $(-2.7\pm 4.7_{\text{stat}}\pm 0.2_{\text{syst}})\times 10^{-5}$ for a local environment of a gravitational potential $\varphi \sim 10^4$ ${\varphi }_{\text{Earth}}$, while that of $\mathrm{G}29-38$ yields $\mathrm{\Delta }\mu /\mu =(-5.8\pm 3.8_{\text{stat}}\pm 0.3_{\text{syst}})\times 10^{-5}$ for a potential of $2\times 10^4$ ${\varphi }_{\text{Earth}}$.

• Received 3 July 2014

DOI:https://doi.org/10.1103/PhysRevLett.113.123002