Domain Walls: Momentum Conservation in Absence of Asymptotic States

Gravitational potentials of the domain walls in the linearized gravity are growing with distance, so the particle scattering by the wall can not be described in terms of free asymptotic states. In the non-relativistic case this problem is solved using the concept of the potential energy. We show that in the relativistic case one is able to introduce gravitationally dressed momenta the sum of which is conserved up to the momentum flux through the lateral surface of the world tube describing losses due to excitation of the branon waves.