Black Holes in Brans-Dicke Theory with a Cosmological Constant

TL;DR

This paper derives black hole solutions with a cosmological constant in Brans-Dicke theory, showing that in four dimensions they match Kerr-Newman-de Sitter solutions with a constant scalar field, but differ in higher dimensions.

Contribution

It introduces the cosmological constant into Brans-Dicke theory via conformal transformation and analyzes the resulting black hole solutions across different dimensions.

Findings

In 4D, solutions are Kerr-Newman-de Sitter with constant scalar field.

In higher dimensions, solutions differ from Kerr-Newman-de Sitter and scalar field is not constant.

In Brans-Dicke-Ni theory, solutions also deviate from Kerr-Newman-de Sitter.

Abstract

Since the Brans-Dicke theory is conformal related to the dilaton gravity theory, by applying a conformal transformation to the dilaton gravity theory, we derived the cosmological constant term in the Brans-Dicke theory and the physical solution of black holes with the cosmological constant. It is found that, in four dimensions, the solution is just the Kerr-Newman-de Sitter solution with a constant scalar field. However, in $n>4$ dimensions, the solution is not yet the $n$ dimensional Kerr-Newman-de Sitter solution and the scalar field is not a constant in general. In Brans-Dicke-Ni theory, the resulting solution is also not yet the Kerr-Newman-de Sitter one even in four dimensions. The higher dimensional origin of the Brans-Dicke scalar field is briefly discussed.