Exact black holes and gravitational shockwaves on codimension-2 branes

We derive exact gravitational fields of a black hole and a relativistic particle stuck on a codimension-2 brane in D dimensions when gravity is ruled by the bulk D-dimensional Einstein-Hilbert action. The black hole is locally the higher-dimensional Schwarzschild solution, which is threaded by a tensional brane 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 the large distance limits of gravity on codimension-2 branes. In an infinite locally flat bulk, they extinguish as 1/rD(-4), i. e. as 1/r(2) on a 3-brane in 6D, manifestly displaying the full dimensionality of spacetime. We check that when we compactify the bulk, this special case correctly reduces to the 4D Aichelburg-Sexl solution at large distances. Our examples show that gravity does not really obstruct having general matter stress-energy on codimension-2 branes, although its mathematical description may be more involved.