  We present the first direct calculation on the gravitational form factors
(GFFs) of the $N \rightarrow \Delta$ transition using an analytic method, the
QCD light-cone sum rules. The matrix element of the quark part of the energy
momentum tensor current sandwiched between the nucleon and $\Delta$ states are
parameterized in terms of five independent conserved and four independent
non-conserved GFFs, for calculation of which we use the distribution amplitudes
(DAs) of the on-shell nucleon expanded in terms of functions with different
twists. We present the results for two sets of light-cone input parameters. The
results indicate that the behavior of the form factors with respect to $Q^2$
are described by multipole fit functions. Our results may be checked by other
phenomenological models including the Lattice QCD as well as future related
experiments.
