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Black Holes in Brans-Dicke Theory with a Cosmological Constant

C. J. Gao·S. N. Zhang
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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.

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C. J. Gao, S. N. Zhang. 2006-04-20. Black Holes in Brans-Dicke Theory with a Cosmological Constant. https://arxiv.org/abs/gr-qc/0604083

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