  We investigate how the gravitational form factors of the nucleon undergo
changes in nuclear matter, emphasizing the Abel transformation from the
three-dimensional (3D) Breit frame to the two-dimensional (2D) light-front
frame. Since the gravitational form factors reveal the mechanical structure of
the nucleon, we examine also the medium modifications of the energy-momentum,
pressure, and shear-force distributions. We scrutinize the stabilities of the
nucleon in nuclear matter. For this purpose, we employ the in-medium modified
SU(2) Skyrme model to study these mechanical quantities of the nucleon, since
it provides a simple but clear framework. In this in-medium modified SU(2)
Skyrme model, the modification of pionic properties is performed by using
low-energy pion-nucleus scattering data and the saturation properties of
nuclear matter near the normal nuclear matter density, $\rho_0=0.5m_\pi^3$. The
results reveal how the nucleon swells in nuclear matter as the mass
distribution of the nucleon is broadened in medium. We also show that the mean
square radii corresponding to the mass and angular momentum distributions
increase in nuclear medium. This feature is kept both in 3D and 2D cases. We
visualize how the strong force fields inside the nucleon in the 2D plane are
distributed and illustrate how these forces undergo change in nuclear matter.
