Constraining a possible time-variation of the gravitational constant   through "gravitochemical heating" of neutron stars
  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. 
Paula Jofre and Andreas Reisenegger (Pontificia Universidad Catolica   de Chile), Rodrigo Fernandez (University of Toronto)