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Form factors of the energy-momentum tensor (EMT) can be interpreted incertain frames in terms of spatial distributions of energy, stress, linear andangular momentum, based on 2D or 3D Fourier transforms. This interpretation isin general subject to "relativistic recoil corrections", except when thenucleon moves at the speed of light like e.g. in the infinite-momentum frame.We show that it is possible to formulate a large-$N_c$ limit in which theprobabilistic interpretation of the nucleon EMT distributions holds also inother frames. We use the bag model formulated in the large-$N_c$ limit as aninternally consistent quark model framework to visualize the informationcontent associated with the 2D EMT distributions. In order to provide moreintuition, we present results in the physical situation and in three differentlimits: by considering a heavy-quark limit, a large system-size limit and aconstituent-quark limit. The visualizations of the distributions in theseextreme limits will help to interpret the results from experiments, latticeQCD, and other models or effective theories.

2D energy-momentum tensor distributions of nucleon in a large-$N_c$ quark model from ultra-relativistic to non-relativistic limit