Holographic massive gravity: solids and fluids
We describe the use of massive gravity theories in the context of gauge/gravity duality as the gravity duals of boundary field theories with momentum dissipation. Of particular interest are massive gravities that correspond to effective field theories describing solids and fluids. The separation between the two can be done both at the level of the unbroken spacetime symmetries as well as concerning the elastic properties of the dual materials. We extract the elastic shear modulus of the black brane solutions in massive gravities of the solid and fluid type and show how it relates to the graviton mass term. We find that the elasticity is non-zero for solids and vanishes for fluids. We then show that the Kovtun-Son-Starinets lower bound on the viscosity to entropy density ratio holds in fluid systems but is clearly violated for solids. To further strengthen the claim that the materials dual to this type of massive gravities are solids, we investigate the spectrum of their quasi-normal modes. We see that by a proper choice of the theory a light transverse phonon—corresponding to the pseudo-Goldstone boson due to the spontaneous breaking of the translational invariance—can be present in the spectrum.