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New spherically symmetric solutions admitting a wormhole throat in Eddington-inspired-Born–Infeld gravity

  • Calvin Tadmon
Research Article
  • 161 Downloads

Abstract

In Schwarzschild coordinates \(\left( t,r,\theta ,\varphi \right) \) on a Lorentzian manifold \({\mathcal {M}}\), we consider a \(\left( t,r\right) \)-dependent real scalar field coupled to an unknown \(\left( t,r\right) \)-dependent physical metric \({\mathbf {g}}\) in the context of Eddington-inspired-Born–Infeld theory of gravity. We derive the complete set of partial differential equations (PDEs) governing the considered system. These are highly nonlinear PDEs whose mathematical analysis is far from easy. We perform a thorough investigation of the static spherically symmetric case and, depending on the sign of the Eddington parameter \(\kappa \), provide new explicit solutions admitting a wormhole throat at some \(r_{0}>0\). In each case the scalar field function \(\psi \) is expressed by means of the normal elliptic integrals of the third kind.

Keywords

Eddington-inspired-Born–Infeld gravity Scalar field Exact static spherically symmetric solutions 

Mathematics Subject Classification

83D05 83F05 

Notes

Acknowledgements

This work was supported by the Abdus Salam International Centre for Theoretical Physics (ICTP, Trieste-Italy) through Associateship programme. I would like to thank Professor Burin Gumjudpai for a discussion on EiBI gravity. Also worthy to be thanked are the two anonymous reviewers for their suggestions that improved the quality of this paper.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of DschangDschangCameroon
  2. 2.International Centre for Theoretical PhysicsTriesteItaly

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