  We study the quantum Hall effect inside a gravitational field. First, we
review the influence of the gravitational field of the Earth on the quantum
Hall effect. Taking the gravitational field of the Earth to be uniform along
the vertical direction, we compute the affected quantized Hall resistivity.
Then, we investigate how the gravitational field modifies the Landau levels of
a particle moving between two massive hemispheres in the presence of a constant
and uniform magnetic field perpendicular to the plane of motion. We find that
the familiar degeneracy of the Landau levels is removed and the spacing between
the latter becomes dependent on the mass density of the hemispheres and on the
gravitational constant $G$. We use this result to show that the quantum Hall
effect in a thin conductor, sandwiched between two massive hemispheres, should
yield a slightly different variation of the Hall resistivity with the applied
magnetic field. We then argue that the well-known problem of the
gravitationally induced electric field, that might a priori be thought to
hinder the effect of gravity, has actually a beneficial role as it amplifies
the latter. We finally discuss whether there is a possibility of using the
quantum Hall effect to probe the inverse-square law of gravity.
