Gravity on codimension 2 brane worlds

We compute the matching conditions for a general thick codimension 2 brane, a necessary previous step towards the investigation of gravitational phenomena in codimension 2 braneworlds. We show that, provided the brane is weakly curved, they are specified by the integral in the extra dimensions of the brane energy-momentum, independently of its detailed internal structure. These general matching conditions can then be used as boundary conditions for the bulk solution. By evaluating Einstein equations at the brane boundary we are able to write an evolution equation for the induced metric on the brane depending only on physical brane parameters and the bulk energy-momentum tensor. We particularise to a cosmological metric and show that a realistic cosmology can be obtained in the simplest case of having just a non-zero cosmological constant in the bulk. We point out several parallelisms between this case and the codimension 1 brane worlds in an AdS space.