The evolution of white dwarfs with a varying gravitational constant
  Within the theoretical framework of some modern unification theories the constants of nature are functions of cosmological time. White dwarfs offer the possibility of testing a possible variation of G and, thus, to place constraints to these theories. We present full white dwarf evolutionary calculations in the case that G decreases with time. White dwarf evolution is computed in a self-consistent way, including the most up-to-date physical inputs, non-gray model atmospheres and a detailed core chemical composition that results from the calculation of the full evolution of progenitor stars. We find that the mechanical structure and the energy balance of white dwarfs are strongly modified by the presence of a varying G. In particular, for certain values of the rate of change of G, the evolution of cool white dwarfs is markedly affected. The impact of a varying G is more notorious in the case of more massive white dwarfs. In view of the recent results reporting that a very accurate white dwarf cooling age can be derived for the old and metal-rich open cluster NGC 6791, our study suggests that this cluster could be a potential target to constrain or detect a ypothetical secular variation of G. 
L. G. Althaus, A. H. Corsico, S. Torres, P. Loren-Aguilar, J. Isern,   and E. Garcia-Berro
astro-ph.SR gr-qc