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We study the energy-momentum tensor of spin-0 and spin-12 hadrons in momentum space. We parametrize this object in terms of so-called gravitational transverse-momentum distributions, and we identify in the quark sector the relations between the latter and the usual transverse-momentum distributions. Focusing on particular components of the energy-momentum tensor, we study momentum densities, flux of inertia and stress distribution in momentum space, revealing part of the wealth of physical information that can be gained from higher-twist transverse-momentum distributions.