Perforation of a domain wall by a point mass

Abstract

We investigate the collision of a point particle and an infinitely thin planar domain wall interacting gravitationally within linearized gravity in a Minkowski space-time of arbitrary dimension. In this setting we are able to describe analytically the perforation of the wall by an impinging particle, showing that it is accompanied by an excitation of the spherical branon shock wave propagating outwards with the speed of light. Formally, the shock wave is a free solution of the branon wave equation which has to be added to ensure the validity of the retarded solution at the perforation point. Physically, the domain wall gets excited due to the shake caused by an instantaneous change of sign of the repulsive gravitational force. This effect is shown to hold, in particular, in four space-time dimensions, which is applicable to the problem of cosmological domain walls.