Model of a Metal in a Gravitational Field

We present a simple model of a metal in a gravitational field in order to show some physical features that help in understanding how the metal holds itself up against gravity. The nuclei are held up against gravity by their bound electron(s) as well as the electric field due to all the gravitationally induced electric dipoles at other lattice sites; these dipoles result from the bound electrons sinking, in response to the gravitational field, by a smaller distance than the nuclei. We also consider the conduction electrons to be held up by Fermi pressure. We use the model to estimate the magnitude of the gravitationally induced electric field in a metal and to establish its direction. We work in the low temperature limit.