  We investigate E1 radiative transitions within charmonium in a relativistic
approach based on light-front QCD. In quantum field theory, two sets of
processes are pure E1: $\chi_{c0} \to J/\psi \gamma$ ($\psi\to
\chi_{c0}\gamma$) and $h_c \to \eta_c\gamma$ ($\eta_c' \to h_c\gamma$), both
involving the $P$-wave charmonia. We compute the E1 radiative decay widths as
well as the corresponding transition form factors of various processes
including those involving $2P$ states. These observables provide an access to
the microscopic structures of the $P$-wave charmonium. We show that our
parameter-free predictions are in excellent agreement with the experimental
measurements as well as lattice simulations whenever available.
