  We argue that Landau-Fermi liquids do not have any gravity duals in the
purely classical limit. We employ the logarithmic behavior of entanglement
entropy to characterize the existence of Fermi surfaces. By imposing the null
energy condition, we show that the specific heat always behaves anomalously. We
also present a classical gravity dual which has the expected behavior of the
entanglement entropy and specific heat for non-Fermi liquids.
