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The electron-graviton interaction can be described in terms of the gravitational form factors of the QED energy-momentum tensor. Here we focus on the form factor D(t), and we examine its properties and its interpretation in terms of internal forces at one-loop accuracy in QED. We perform the calculation by keeping separate the contributions due to the electron and the photon parts of the energy-momentum tensor. We also study the case of a nonzero photon mass. Furthermore, we discuss similarities with and differences to the form factor D(t) of hadronic bound states.