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A hypothetical time-variation of the gravitational constant $G$ would makeneutron stars expand or contract, so the matter in their interiors would departfrom beta equilibrium. This induces non-equilibrium weak reactions, whichrelease energy that is invested partly in neutrino emission and partly ininternal heating. Eventually, the star arrives at a stationary state in whichthe temperature remains nearly constant, as the forcing through the change of$G$ is balanced by the ongoing reactions. Using the surface temperature of thenearest millisecond pulsar (PSR J0437$-$4715) inferred from ultravioletobservations and results from theoretical modelling of the thermal evolution,we estimate two upper limits for this variation: (1) $|\dot G/G| < 2 \times10^{-10}\mathrm{yr}^{-1},$ if the fast, "direct Urca" reactions are allowed,and (2) $|\dot G/G|<4\times 10^{-12}\mathrm{yr}^{-1},$ considering only theslower, "modified Urca" reactions. The latter is among the most restrictiveupper limits obtained by other methods.

Constraining a possible time-variation of the gravitational constant through "gravitochemical heating" of neutron stars