Exact black holes and gravitational shockwaves on codimension-2 branes

We derive exact gravitational fields of a black hole and a relativisticparticle stuck on a codimension-2 brane in $D$ dimensions when gravity is ruledby the bulk $D$-dimensional Einstein-Hilbert action. The black hole is locallythe higher-dimensional Schwarzschild solution, which is threaded by a tensionalbrane yielding a deficit angle and includes the first explicit example of a`small' black hole on a tensional 3-brane. The shockwaves allow us to study thelarge distance limits of gravity on codimension-2 branes. In an infinitelocally flat bulk, they extinguish as $1/r^{D-4}$, i.e. as $1/r^2$ on a 3-branein $6D$, manifestly displaying the full dimensionality of spacetime. We checkthat when we compactify the bulk, this special case correctly reduces to the 4DAichelburg-Sexl solution at large distances. Our examples show that gravitydoes not really obstruct having general matter stress-energy on codimension-2branes, although its mathematical description may be more involved.Comment: 18 pages, LaTeX; v2: added references, version to appear in JHE