  Relativistic jets, or highly collimated and fast-moving outflows, are endemic
to many astrophysical phenomena. The jets produced by gamma-ray bursts and
tidal disruption events are accompanied by the accretion of material onto a
black hole or neutron star, with the accretion rate exceeding the Eddington
limit of the compact object by orders of magnitude. In such systems, radiation
dominates the energy-momentum budget of the outflow, and the dynamical
evolution of the jet is governed by the equations of radiation hydrodynamics.
Here we show that there are analytic solutions to the equations of radiation
hydrodynamics in the viscous (i.e., diffusive) regime that describe structured,
relativistic jets, which consist of a fast-moving, highly relativistic core
surrounded by a slower-moving, less relativistic sheath. In these solutions,
the slower-moving, outer sheath contains most of the mass, and the jet
structure is mediated by local anisotropies in the radiation field. We show
that, depending on the pressure and density profile of the ambient medium, the
angular profile of the jet Lorentz factor is Gaussian or falls off even more
steeply with angle. These solutions have implications for the nature of jet
production and evolution in hyperaccreting systems, and demonstrate that such
jets -- and the corresponding jet structure -- can be sustained entirely by
radiative processes. We discuss the implications of these findings in the
context of jetted tidal disruption events and short and long gamma-ray bursts.
