The light-cone spreading of entanglement and correlation is a
fundamental and ubiquitous feature of homogeneous extended quantum
systems. Here we point out that a class of inhomogenous Luttinger
liquids (those with a uniform Luttinger parameter K) at low energy
display the universal phenomenon of curved light cones: gapless
excitations propagate along the null geodesics of the metric ds(2) = d
x(2) - v (x)(2)d t(2), with v (x) being the calculable spatial dependent
velocity induced by the inhomogeneity. We confirm our findings with
explicit analytic and numerical calculations both in-and
out-of-equilibrium for a Tonks-Girardeau gas in a harmonic potential and
in lattice systems with artificially tuned hamiltonian density
