  In this paper, following hep-th/0501028, we present a detailed derivation and
discussion of the exact gravitational field solutions for a relativistic
particle localized on a tensional brane in brane-induced gravity. Our
derivation yields the metrics for both the normal branch and the self-inflating
branch DGP braneworlds. They generalize the 4D gravitational shock waves in de
Sitter space, and so we compare them to the corresponding 4D General Relativity
solution and to the case when gravity resides only in the 5D bulk, and there
are no brane-localized graviton kinetic terms. We write down the solutions in
terms of two-variable hypergeometric functions and find that at short distances
the shock wave profiles look exactly the same as in 4D Minkowski space, thus
recovering the limit one expects if gravity is to be mediated by a metastable,
but long-lived, bulk resonance. The corrections far from the source differ from
the long distance corrections in 4D de Sitter space, coming in with odd powers
of the distance. We discuss in detail the limiting case on the self-inflating
branch when gravity is modified exactly at de Sitter radius, and energy can be
lost into the bulk by resonance-like processes. Finally, we consider Planckian
scattering on the brane, and find that for a sufficiently small impact
parameter it is approximated very closely by the usual 4D description.
