  We present new analytic solutions to the relativistic Boltzmann equation
within the relaxation time approximation. We first obtain spherically expanding
solutions which are the kinetic counterparts of the exact solutions of the
Israel-Stewart equation in the literature. This allows us to compare the
solutions of the kinetic and hydrodynamic equations at an analytical level. We
then derive a novel boost-invariant solution of the Boltzmann equation which
has an unconventional dependence on the proper time. The existence of such a
solution is also suggested in second order hydrodynamics and fluid-gravity
correspondence.
