  We study the holographic entanglement entropy and mutual information for
Lorentz boosted subsystems. In holographic CFTs at zero and finite temperature,
we find that the mutual information gets divergent in a universal way when the
end points of two subsystems are light-like separated. In Lifshitz and
hyperscaling violating geometries dual to non-relativistic theories, we show
that the holographic entanglement entropy is not well-defined for Lorentz
boosted subsystems in general. This strongly suggests that in non-relativistic
theories, we cannot make a real space factorization of the Hilbert space on a
generic time slice except the constant time slice, as opposed to relativistic
field theories.
