  We analyze the range of validity of Thomas Fermi theory for describing charge
density modulations induced by external potentials in neutral graphene. We
compare exact results obtained from a tight-binding calculation with those of
linear response theory and the Thomas Fermi approximation. For experimentally
interesting ranges of size and density amplitudes (electron densities less than
$\sim 10 ^{11} cm ^{-2}$, and spatial length scales below $\sim 20 nm$), linear
response is significantly more accurate than Thomas Fermi theory.
