  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 as the
``gravitational form factors'', 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 gravitational form factors for a
hadron, in particular, for a (pseudo)scalar hadron and for the nucleon. We
derive and clarify the relations satisfied by the gravitational form factors as
direct consequences of the symmetries and the equations of motion in QCD, and
connections to the generalized parton distributions. Our results reveal that
the gravitational form factors are related to the higher-twist quark-gluon
correlation effects inside the hadrons and also to QCD trace anomaly.
