A hypothetical time-variation of the gravitational constant G would make neutron stars expand or contract , so the matter in their interiors would depart from beta equilibrium .
This induces non-equilibrium weak reactions , which release energy that is invested partly in neutrino emission and partly in internal heating .
Eventually , the star arrives at a stationary state in which the temperature remains nearly constant , as the forcing through the change of G is balanced by the ongoing reactions .
Using the surface temperature of the nearest millisecond pulsar ( PSR J0437 - 4715 ) inferred from ultraviolet observations and results from theoretical modelling of the thermal evolution , we estimate two upper limits for this variation : ( 1 ) | \dot { G } / G| < 2 \times 10 ^ { -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 the slower , “ modified Urca ” reactions .
The latter is among the most restrictive upper limits obtained by other methods .