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Nonlinearly charged dilatonic black holes and their Brans–Dicke counterpart: energy dependent spacetime

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Abstract

Regarding the wide applications of dilaton gravity in the presence of electrodynamics, we introduce a suitable Lagrangian for the coupling of dilaton with gauge field. There are various Lagrangians which show the coupling between scalar fields and electrodynamics with correct special situations. In this paper, taking into account conformal transformation of Brans–Dicke theory with an electrodynamics Lagrangian, we show that how scalar field should couple with electrodynamics in dilaton gravity. In other words, in order to introduce a correct Lagrangian of dilaton gravity, one should check at least two requirements: compatibility with Brans–Dicke theory and appropriate special situations. Finally, we apply the mentioned method to obtain analytical solutions of dilaton-Born–Infeld and Brans–Dicke–Born–Infeld theories with energy dependent spacetime.

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Acknowledgements

We would like to thank an anonymous referee for suggesting important improvements. MST is indebted to M. Kord Zangeneh for useful discussions. We also thank the Shiraz University Research Council. This work has been supported financially by the Research Institute for Astronomy and Astrophysics of Maragha, Iran.

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Authors and Affiliations

  1. Physics Department and Biruni Observatory, College of Sciences, Shiraz University, Shiraz, 71454, Iran

    S. H. Hendi & M. S. Talezadeh

  2. Research Institute for Astrophysics and Astronomy of Maragha (RIAAM), P.O. Box 55134-441, Maragha, Iran

    S. H. Hendi

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  1. S. H. Hendi
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  2. M. S. Talezadeh
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Correspondence to S. H. Hendi.

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Hendi, S.H., Talezadeh, M.S. Nonlinearly charged dilatonic black holes and their Brans–Dicke counterpart: energy dependent spacetime. Gen Relativ Gravit 49, 12 (2017). https://doi.org/10.1007/s10714-016-2176-5

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