Branestrahlung: Radiation in the particle-brane collision

Abstract

We calculate the radiation accompanying the gravitational collision of a domain wall a the point particle in five-dimensional spacetime. This process -which can be regarded as brane-particle bremsstrahlung, here called branestrahlung -has unusual features. Since the brane has intrinsic dynamics, it gets excited in the course of collision, and, in particular, at the moment of perforation the shock branon wave is generated, which then expands with the velocity of light. Therefore, apart from the time-like source whose radiation can be computed in a standard way, the total radiation source contains a light-like part whose retarded field is quite nontrivial, exhibiting interesting retardation and memory effects. We analyze this field in detail, showing that -contrary to the claims that the light-like sources should not radiate at all -the radiation is nonzero and has classically divergent spectrum. We estimate the total radiation power introducing appropriate cutoffs. In passing, we explain how the sum of the nonlocal (with the support inside the light cone) and the local (supported on the cone) singular parts of the Green's function of the five-dimensional d'Alembert equation together defines a regular functional.

Piercing of domain walls: new mechanism of gravitational radiation

“…Our space-time is not asymptotically flat, so one should revisit the derivation. In particular, the energy-momentum flux through the lateral surface of the world-tube turns out to be non-zero [34]. Meanwhile, one can transform the flux at infinity, when it is well defined, into the volume integral extended through the space-time.…”

“…Still it turned out possible to introduce the dressed momenta for both objects which are instantaneously conserved during the collision [33]. We also calculated emission of scalar waves under perforation assuming that the particle (but not the wall) to interact with a scalar field apart of gravity [34].…”

“…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, .…”

“…Similarly we can present the change of the momentum of the wall, this quantity is assumed to be finite, while the momentum itself is infinite (for more detailed discussion see [34]). Using the eq.…”

“…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.…”