ИСТИНА

In the linearized theory gravitational potentials of the domain walls are growing with distance,so their interaction with particles constitutes a peculiar scattering problem without asymptotic states. In non-relativisting case this problem is solved via introduction of the potential energy. We show, that in the relativistic case, treating gravity perturbatively in Minkowski space, one is able to introduce relativistic analog of the potential energy of the particle in the field of the domain wall, and respectively, of the domain wall in the gravitational field of the particle, treating them as interacting objects on equal footing. Subtracting the infinite momentum associated with the bare wall, one is able to extract finite parts of the interaction momentum and to present the full momentum as a sum of kinetic and potential terms. Similar procedure applies for the particle. The sum of total momenta defined in this way is conserved up to an extra lateral flux arising due to an infinite extension of the wall.