  In many-body fermionic systems at finite density correlation functions of the
density operator exhibit Friedel oscillations at a wavevector that is twice the
Fermi momentum. We demonstrate the existence of such Friedel oscillations in a
3d gravity dual to a compressible finite-density state in a (1+1) dimensional
field theory. The bulk dynamics is provided by a Maxwell U(1) gauge theory and
all the charge is behind a bulk horizon. The bulk gauge theory is compact and
so there exist magnetic monopole tunneling events. We compute the effect of
these monopoles on holographic density-density correlation functions and
demonstrate that they cause Friedel oscillations at a wavevector that directly
counts the charge behind the bulk horizon. If the magnetic monopoles are taken
to saturate the bulk Dirac quantization condition then the observed Fermi
momentum exactly agrees with that predicted by Luttinger's theorem, suggesting
some Fermi surface structure associated with the charged horizon. The mechanism
is generic and will apply to any charged horizon in three dimensions. Along the
way we clarify some aspects of the holographic interpretation of Maxwell
electromagnetism in three bulk dimensions and show that perturbations about the
charged BTZ black hole exhibit a hydrodynamic sound mode at low temperature.
