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

Linear Response and the Thomas-Fermi Approximation in Undoped Graphene