  Understanding the internal structure of nucleons and nuclei has been a topic
of enduring interest in high-energy physics. Gravitational form factors (GFFs)
provide an important portal for us to probe the energy-momentum/mass
distribution of nucleons and nuclei. This letter presents the study of the
photon and gluon momentum GFFs, also known as the A-GFFs, of relativistic
hadrons using the Weizs\"acker-Williams method. To begin, we express the photon
A-GFFs in terms of charge form factors and discuss the corresponding photon
radius. Furthermore, an integral relation between the gluon A-GFF and the
Laplacian of dipole scattering amplitude is derived in the small-$x$ framework,
and it allows us to unravel the gluon energy momentum distribution inside
hadrons through measurements at the upcoming Electron-Ion Collider. In
addition, we generalize the analysis to study the A-GFF of nuclei and propose
employing the nuclear gluon mean square radius, together with the charge
distribution, to constrain the neutron distribution for large nuclei. This work
provides an interesting perspective into the fundamental structure of
high-energy hadrons.
