  The gravitational form factors for a hadron, the form factors for the hadron
matrix element of the QCD energy-momentum tensor, not only describe the
coupling of the hadron with a graviton, but also serve as unique quantities for
describing the shape inside the hadron reflecting dynamics of quarks and
gluons, such as the internal shear forces acting on the quarks/gluons and their
pressure distributions. We consider the quark contribution to the gravitational
form factors for a (pseudo)scalar hadron, and derive and clarify the relations
satisfied by them as direct consequences of the symmetries and the equations of
motion in QCD, and connections to the generalized parton distributions. Our
results reveal the connections between the gravitational form factors and the
higher-twist quark-gluon correlation effects inside the hadrons.
