  The Reissner-Nordstrom black hole provides the prototypical description of a
holographic system at finite density. We study the response of this system to
the presence of a local, charged impurity. Below a critical temperature, the
induced charge density, which screens the impurity, exhibits oscillations.
These oscillations can be traced to the singularities in the density-density
correlation function moving in the complex momentum plane. At finite
temperature, the oscillations are very similar to the Friedel oscillations seen
in Fermi liquids. However, at zero temperature the oscillations in the black
hole background remain exponentially damped, while Friedel oscillations relax
to a power-law
