Kerr-Newman-de Sitter Solution on DGP Brane

TL;DR

This paper derives an exact Kerr-Newman-de Sitter solution on a DGP braneworld, demonstrating its properties under various conditions and its implications for accelerated expansion in the universe.

Contribution

It provides the first exact Kerr-Newman-de Sitter solution on a DGP brane with a detailed analysis of its properties and behavior under coordinate transformations.

Findings

Solution is well-behaved under Boyer-Lindquist transformation.

Only zero (flat) and positive (de Sitter) Ricci scalar values satisfy the Hamiltonian constraint.

In the non-rotating limit, the solution indicates accelerated expansion of the universe.

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 Z_2-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.