  In cosmological models with a varying gravitational constant, it is not clear
whether primordial black holes preserve the value of $G$ at their formation
epoch. We investigate this question by using the Tolman-Bondi model to study
the evolution of a background scalar field when a black hole forms from the
collapse of dust in a flat Friedmann universe. Providing the back reaction of
the scalar field on the metric can be neglected, we find that the value of the
scalar field at the event horizon very quickly assumes the background
cosmological value. This suggests that there is very little gravitational
memory.
