  We extend the standard second order effective chiral Lagrangian of pions and
nucleons by considering the coupling to an external gravitational field. As an
application we calculate one-loop corrections to the one-nucleon matrix element
of the energy-momentum tensor to fourth order in chiral counting, and
next-to-leading order tree-level amplitude of the pion-production in an
external gravitational field. We discuss the relation of the obtained results
to experimentally measurable observables. Our expressions for the chiral
corrections to the nucleon gravitational form factors differ from those in the
literature. That might require to revisit the chiral extrapolation of the
lattice data on the nucleon gravitational form factors obtained in the past.

High Energy Physics - Phenomenology;High Energy Physics - Lattice;Nuclear Theory