  Recently, it has been realized that liquids are able to support solid-like
transverse modes with an interesting gap in momentum space developing in the
dispersion relation. We show that this gap is also present in simple
holographic bottom-up models, and it is strikingly similar to the gap in
liquids in several respects. Firstly, the appropriately defined relaxation time
in the holographic models decreases with temperature in the same way. More
importantly, the holographic $k$-gap increases with temperature and with the
inverse of the relaxation time. Our results suggest that the Maxwell-Frenkel
approach to liquids, involving the additivity of liquid hydrodynamic and
solid-like elastic responses, can be applicable to a much wider class of
physical systems and effects than thought previously, including relativistic
models and strongly-coupled quantum field theories. More precisely, the
dispersion relation of the propagating shear waves is in perfect agreement with
the Maxwell-Frenkel approach. On the contrary the relaxation time appearing in
the holographic models considered does not match the Maxwell prediction in
terms of the shear viscosity and the instantaneous elastic modulus but it
shares the same temperature dependence.
