Perforation of a domain wall by a point mass

Abstract

We investigate collision of a point particle and an infinitely thin planar domain wall interacting gravitationally within the linearized gravity in 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 excitation of the spherical shock branon 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, being applicable to the problem of cosmological domain walls.

Piercing of domain walls: new mechanism of gravitational radiation

“…For D = 4 these two integrals diverge logarithmically, though, as it was shown in [32], the corresponding regularized solutions exist. Here we will use the direct solution of the eq.…”

“…We keep notation introduced in the previous papers [32][33][34]. The (D − 2)-dimensional DW propagating in the D-dimensional space-time M D with the metric g M N , has the worldvolume V D−1 parametrized by arbitrary coordinates σ µ , µ = 0, 1, 2, .…”

“…This approach opens a way to describe analytically the branon excitation of the wall revealing creation of the free branon wave. This phenomenon was first found within the RS II five-dimensional model [31] and then generalized to arbitrary dimensions [32] showing that the branon effects are dimension-dependent in view of the different causal structure of propagators of massless fields in even and odd space-time dimensions [35][36][37]. The particle-DW interaction has the growing potential, so there are no free asymptotic states.…”

“…We use the framework first suggested in [31] and further developed in [32][33][34], which essentially consists of perturbative description of gravitational interaction of the Nambu-Goto DW and the classical point particle in Minkowski space. This approach opens a way to describe analytically the branon excitation of the wall revealing creation of the free branon wave.…”

“…Note, the zeroth-order field in our model is Minkowskian everywhere. This fact preserves the conservation laws [32,33], and the dynamics of particle and brane is self-consistent. But if we consider times t > L ≡ z max in RSII-setting, the free particle after the shock collision moves in the true RSII-metric which is exponentially decaying.…”