Abstract: Inspired by the scattering amplitude program applied to General Relativity, we define the most generic energy-momentum tensor at linear order constructed by mass and spin in momentum space and arbitrary dimensions. Through this approach, we establish a one-to-one correspondence between the form factors that characterize the source and the gravitational multipole moments of the induced spacetime, providing a precise definition of source multipoles in a relativistic context and identifying a new class of "stress" multipoles. We then apply this formalism to build physically reasonable sources of black hole mimickers.