  We extend our relativistic theory of gravitational structure of composite
hadrons to obtain the pion gravitational form factors at large momentum
transfers. The approach was used in the case of intermediate region of the
variable in our preceding works arXiv:2010.11640 and arXiv:2201.04991. The
calculation is carried out in the framework of a relativistic
composite-particle model complemented by the special relativistic form of
impulse approximation. It is found that in the limit of massless and pointlike
quarks, the obtained asymptotic expansion coincides with the predictions of
perturbative QCD for gravitational pion form factors. The principal
contribution to the asymptotics, coinciding with the predictions of QCD, is
given by the relativistic effect of spin rotation. In particular, the
asymptotics of the D form factor is completely determined by this kinematic
effect. Several constraints on the allowed form of gravitational form factors
of quarks are derived.
