Kerr–Newman–de Sitter solution on DGP brane

Abstract

We find an exact solution of Kerr–Newman–de Sitter type on the braneworld (4D) of the DGP model. When a constant 4D Ricci scalar is assumed, only zero (flat) and a positive (de Sitter) values satisfy the Hamiltonian constraint equation coming from the extra dimension. With a Z2-symmetry across the brane and a stationary and axisymmetric metric ansatz on the brane, we solve the constraint equation exactly in the Kerr–Schild form with de Sitter background. In the de Sitter background this Kerr–Schild solution is well behaved under Boyer–Lindquist transformation: the constraint equation is preserved under the transformation and so is the solution. In the non-rotating limit we show that this Kerr–Newman–de Sitter solution has the characteristic of accelerated expansion of the braneworld universe.