In the weak interaction limit, behaviors of electrons can still
be described by a 1-partitcle equation with a modified mass,
where the change in mass can be understood as effects of other
neighboring electrons as a single electron drags along. Since
the cluster of electrons couples to gravity as usual, then the
effective mass of a quasi-particle couples to gravity in the
same way as that of a genuine electron. Moreover, the effective
mass can be negative which is the case of holes which are
“bubbles” in the electron liquid. In graphene, there are
massless Dirac electrons. Do they couple to the gravity? I think
what I intended to ask should be "How to incorporate effects of
gravity in a many-electron system?" (Originally I asked "do
effective masses couple to gravity?")