Energy-momentum balance in particle - domain wall perforating collision

We investigate the energy-momentum balance in the perforating collision of a point particle with an infinitely thin planar domain wall within the linearized gravity in arbitrary dimensions. Since the metric of the wall increases with distance, the wall and the particle are never free, and their energy-momentum balance involves not only the instantaneous kinetic momenta, but also the non-local contribution of gravitational stresses. However, careful analysis shows that the stresses can be unambiguously divided between the colliding objects leading to definition of the gravitationally dressed momenta. These take into account for gravity in the same way as the potential energy does in the non-relativistic theory, but our treatment is fully relativistic. Another unusual feature of our problem is the non-vanishing flux of the total energy-momentum tensor through the lateral surface of the world tube. In this case the zero divergence of the energy-momentum tensor does not imply conservation of the total momentum defined as the integral over the space-like section of the tube. But one can still define the conservation low infinitesimally, passing to time derivatives of the momenta. Using this definition we establish the momentum balance in terms of the dressed particle and wall momenta.