Weak gravity in the Dvali-Gabadadze-Porrati braneworld model

We analyze weak gravity in the braneworld model proposed by Dvali, Gabadadze, and Porrati, in which the unperturbed background spacetime is given by a five-dimensional Minkowski bulk with a brane which has an induced Einstein-Hilbert term. This model has a critical length scale $r_c.$ Naively, we expect that four-dimensional general relativity (4D GR) is approximately recovered at a scale below $r_c.$ However, the simple linear perturbation does not work in this regime. Only recently has the mechanism to recover 4D GR been clarified under the restriction to spherically symmetric configurations, and the leading correction to 4D GR been derived. Here, we develop an alternative formulation which can handle more general perturbations. We also generalize the model by adding a bulk cosmological constant and the brane tension.