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International Journal of Theoretical Physics

, Volume 51, Issue 8, pp 2380–2391 | Cite as

On Effective Potential in Tortoise Coordinate

  • M. A. Ganjali
Article

Abstract

In this paper, we study the field dynamics in Tortoise coordinate where the equation of motion of a scalar can be written as Schrodinger-like form. We obtain a general form for effective potential by finding the Schrodinger equation for scalar and spinor fields and study its global behavior in some black hole backgrounds in three dimension such as BTZ black holes, new type black holes and black holes with no horizon.

Especially, we study the asymptotic behavior of potential at infinity, horizons and origin and find that its asymptotic in BTZ and new type solution is completely different from that of vanishing horizon solution. In fact, potential for vanishing horizon goes to a fixed quantity at infinity, while in BTZ and new type black hole we have an infinite barrier.

Keywords

Tortoise coordinate Scalar field dynamics Effective potential Black hole Fermionic field 

Notes

Acknowledgements

I would like to thank Dr. Fareghbal for useful comments. I also like to thank Dr. Kanjouri due to his guides in plotting the figures.

This work is supported by the “Grant for Research Projects” in Tarbiat Moallem University.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Fundamental SciencesTarbiat Moaallem UniversityTehranIran

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