A hypothetical time-variation of the gravitational constant G would cause neutron star matter to depart from beta equilibrium , due to the changing hydrostatic equilibrium .
This forces non-equilibrium beta processes to occur , which release energy that is invested partly in neutrino emission and partly in heating the stellar interior .
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 .
Comparing the surface temperature of the nearest millisecond pulsar , PSR J0437-4715 , inferred from ultraviolet observations , with our predicted stationary temperature , we estimate two upper limits for this variation : ( 1 ) | \dot { G } / G| < 2 \times 10 ^ { -10 } yr ^ { -1 } , if we allow direct Urca reactions operating in the neutron star core , and ( 2 ) | \dot { G } / G| < 4 \times 10 ^ { -12 } yr ^ { -1 } , considering only modified Urca reactions .
Both results are competitive with those obtained by other methods , with ( 2 ) being among the most restrictive .