  A future Electron-Ion Collider will enable the gluon contributions to the
gravitational form factors of the proton to be constrained experimentally for
the first time. Here, the first calculation of these form factors from lattice
Quantum Chromodynamics is presented. The calculations use a
larger-than-physical value of the light quark mass corresponding to $m_\pi \sim
450$ MeV. All three form factors, which encode the momentum-dependence of the
lowest moment of the spin independent gluon generalised parton distributions
and are related to different components of the energy-momentum tensor, are
resolved. In particular, the gluon $D$-term form factor, related to the
pressure distribution inside the nucleon, is determined for the first time. The
gluon contributions to the two gravitational form factors of the pion are also
determined, and are compared to existing lattice determinations of the quark
contributions to the gravitational form factors and to phenomenology.
