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Spherically Symmetric Solutions of Light Galileon

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Abstract

We have been studied the model of light Galileon with translational shift symmetry ϕ → ϕ + c. The matter Lagrangian is presented in the form \(\mathcal {L}_{\phi }= -\eta (\partial \phi )^{2}+\beta G^{\mu \nu }\partial _{\mu }\phi \partial _{\nu }\phi \). We have been addressed two issues: the first is that, we have been proven that, this type of Galileons belong to the modified matter-curvature models of gravity in type of \(f(R,R^{\mu \nu }T_{\mu \nu }^{m})\). Secondly, we have been investigated exact solution for spherically symmetric geometries in this model. We have been found an exact solution with singularity at r = 0 in null coordinates. We have been proven that the solution has also a non-divergence current vector norm. This solution can be considered as an special solution which has been investigated in literature before, in which the Galileon’s field is non-static (time dependence). Our scalar-shift symmetrized Galileon has the simple form of ϕ = t, which it is remembered by us dilaton field.

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Notes

  1. We changed the singnature to kept the regularity of our work

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Acknowledgments

We gratefully acknowledge M. Sami and S. D. Odintsov for useful comments. Manuel E. Rodrigues thanks UFPA, Edital 04/2014 PROPESP, and CNPq, Edital MCTI/CNPQ/Universal 14/2014, for partial financial support.

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Authors and Affiliations

  1. Eurasian International Center for Theoretical Physics and Department of General & Theoretical Physics, Eurasian National University, Astana, 010008, Kazakhstan

    D. Momeni & R. Myrzakulov

  2. Institut de Mathématiques et de Sciences Physiques (IMSP), 01 BP 613, Porto-Novo, Benin

    M. J. S. Houndjo

  3. Faculté des Sciences et Techniques de Natitingou, Université de Parakou, Parakou, Benin

    M. J. S. Houndjo

  4. Department of Physics, Istanbul University, Istanbul, Turkey

    E. Güdekli

  5. Faculdade de Ciências Exatas e Tecnologia, Universida de Federal do Pará Campus Universitário de Abaetetuba, CEP 68440-000, Abaetetuba, Pará, Brazil

    M. E. Rodrigues

  6. Departamento de Engenharia e Ciências Naturais - CEUNES, Universidade Federal do Esp ́rito Santo, CEP 29933-415, São Mateus/ ES, Brazil

    F. G. Alvarenga

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  1. D. Momeni
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  2. M. J. S. Houndjo
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  3. E. Güdekli
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  4. M. E. Rodrigues
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  5. F. G. Alvarenga
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  6. R. Myrzakulov
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Momeni, D., Houndjo, M.J.S., Güdekli, E. et al. Spherically Symmetric Solutions of Light Galileon. Int J Theor Phys 55, 1211–1221 (2016). https://doi.org/10.1007/s10773-015-2762-4

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