**Author details** Retracted

Pınar Kirezli Uludağ Department of Physics, Namık Kemal University, Tekirdağ, Turkey

\*Address all correspondence to: pkirezli@nku.edu.tr

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Brans-Dicke Solutions of Stationary, Axially Symmetric Spacetimes DOI: http://dx.doi.org/10.5772/intechopen.89906*

#### **References**

**4. GR limit of the solutions**

*Advances on Tensor Analysis and Their Applications*

the corresponding GR ones.

equations should be provided.

limit of these solutions.

**Author details**

**44**

Pınar Kirezli Uludağ

**5. Conclusion**

According to the common belief, since BD parameter *ω* ! ∞, the BD solutions reduce to corresponding GR ones. Contrary to this belief, several counter examples were presented in the literature [20–24]. In our study, the GR limit of the BD solutions is out of complexity. When *k* ! 1, BD transformation equations of (44)– (46) reduce to seed GR metric functions for any finite *ω* since scalar field *ϕ* becomes constant. It is obvious from the given examples that, as *k* ! 1, BD metrics reduce

In this section, we have studied to obtain corresponding BD or BD-Maxwell solution from any known solution of the Einstein or the Einstein-Maxwell theory for stationary, axially symmetric spacetimes in Jordan frame. First we present that, although several field equations of BD are not included by Ernst equations, BD field equations can be written in the form of Ernst Eqs. BD solutions can be obtained by selecting the appropriate physical potentials or by integrating Ernst equations, but it should be remembered that the equations which are not included in the Ernst

In order to obtain BD solutions, we have constructed two parameter solutiongenerating techniques. It was seen that, in previous works, it was studied with one parameter. From any given seed GR solution of Eqs. (6) or (20), the corresponding BD solution can be obtained by the two parameter solution-generating techniques. In order to show how this method works, we have constructed several known solutions and also some new solutions for BD theory. We have also discussed the GR

Department of Physics, Namık Kemal University, Tekirdağ, Turkey

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

\*Address all correspondence to: pkirezli@nku.edu.tr

provided the original work is properly cited.

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