Pomeranchuk instability from a black hole

Within the AdS/CFT correspodence, we introduce a probe spinor field and a neutral symmetric traceless spin-two field which are dual to a fermionic operator and a neutral tensor order parameter in the boundary field theory. By considering a certain coupling between the two probe fields, we show that a transition induced by condensation of the neutral order parameter dual to the neutral spin-two field can lead to the breaking of rotational symmetry of Fermi surface and hence a Pomeranchuk instability. The critical properties of this transition are computed.