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Rastall’s theory of gravity: spherically symmetric solutions and the stability problem

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Abstract

We study the stability of static, spherically symmetric solutions of Rastall’s theory in the presence of a scalar field with respect to spherically symmetric perturbations. The analysis of perturbations shows that there arises an inconsistency in the sense that time-dependent perturbations do not exist in any order of perturbation theory, and we can conclude that these solutions are pertubatively stable (though nonperturbative time-dependent solutions are not excluded). Possible reasons for this inconsistency are discussed.

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Notes

  1. The Rastall parameter a is related to the other frequently used parameter \(\lambda \) by \(a = \dfrac{3\lambda -2}{2\lambda -1}\).

References

  1. Rastall, P.: Phys. Rev. D 6, 3357 (1972)

    Article  ADS  MathSciNet  Google Scholar 

  2. Silva, G.F., Piattella, O.F., Fabris, J.C., Casarini, L., Barbosa, T.O.: Grav. Cosmol. 19, 156 (2013)

    Article  ADS  Google Scholar 

  3. Batista, C.E.M., Daouda, M.H., Fabris, J.C., Piattella, O.F., Rodrigues, Davi C.: Phys. Rev. D85, 084008 (2012)

    ADS  Google Scholar 

  4. Gao, C., Kunz, M., Liddle, A.R., Parkinson, D.: Phys. Rev. D 81, 043520 (2010)

    Article  ADS  Google Scholar 

  5. Bronnikov, K.A., Fabris, J.C., Piattella, O.F., Santos, E.: Gen. Rel. Gravit. 48, 162 (2016)

    Article  ADS  Google Scholar 

  6. Bronnikov, K.A., Fabris, J.C., Rodrigues, Denis C.: Grav. Cosmol. 22, 26 (2016)

    Article  ADS  Google Scholar 

  7. Bronnikov, K.A., Fabris, J.C., Piattella, O.F., Rodrigues, Denis C., Santos, E.C.: Eur. Phys. J. C 77, 409 (2017)

    Article  ADS  Google Scholar 

  8. Bronnikov, K.A., Fabris, J.C., Rodrigues, Denis C.: Int. J. Mod. Phys. D 29, 2050016 (2020)

    Article  ADS  Google Scholar 

  9. Fabris, J.C., Daouda, M.H., Piattella, O.F.: Phys. Lett. B 711, 232 (2012)

    Article  ADS  Google Scholar 

  10. Gonzalez, J.A., Guzman, F.S., Sarbach, O.: Class. Quantum Grav. 26, 015010 (2009). arXiv: 0806.0608

    Article  ADS  Google Scholar 

  11. Bronnikov, K.A., Fabris, J.C., Zhidenko, A.: Eur. Phys. J. C 71, 1791 (2011). arXiv: 1109.6576

    Article  ADS  Google Scholar 

  12. Bronnikov, K.A.: Particles 2018, 1, 5 (2018); arXiv: 1802.00098

  13. Smalley, L.: Il Nuovo Cimento B 80, 42 (1984)

    Article  ADS  Google Scholar 

  14. dos Santos, R.V., Nogales, J.A.C.: Cosmology from a Lagrangian formulation for Rastall’s theory. arXiv: 1701.08203

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Acknowledgements

J.C. Fabris and O.F. Piattella thank CNPq (Brazil) and FAPES (Brazil) for partial financial support. D.C. Rodrigues was financed in part by the Coordenação de Aperfeitoamento de Pessoal de Nível Superior—Brasil (CAPES)—Finance Code 001. E.C.O. Santos thanks FAPES (Brazil) for financial support. The work of K. Bronnikov was supported by the RUDN University program 5-100 and by the Russian Foundation for Basic Research Project 19-02-00346. The work of K.B. was also performed within the framework of the Center FRPP supported by MEPhI Academic Excellence Project (Contract Nos. 02.a03.21.0005, 27.08.2013).

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Authors and Affiliations

  1. Center of Gravitation and Fundamental Metrology, VNIIMS, Ozyornaya ul. 46, Moscow, Russia, 119361

    K. A. Bronnikov

  2. Institute of Gravitation and Cosmology, Peoples’ Friendship University of Russia (RUDN University), ul. Miklukho-Maklaya 6, Moscow, Russia, 117198

    K. A. Bronnikov

  3. National Research Nuclear University “MEPhI”, Kashirskoe sh. 31, Moscow, Russia, 115409

    K. A. Bronnikov & Júlio C. Fabris

  4. Núcleo Cosmo-ufes & Departamento de Física, CCE, Universidade Federal do Espírito Santo, Vitória, ES, CEP 29075-910, Brazil

    Júlio C. Fabris & Oliver F. Piattella

  5. PPGFis, CCE, Universidade Federal do Espírito Santo, Vitória, ES, CEP 29075-910, Brazil

    Denis C. Rodrigues

  6. PPGCosmo, CCE, Universidade Federal do Espírito Santo, Vitória, ES, CEP 29075-910, Brazil

    Edison C. O. Santos

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  1. K. A. Bronnikov
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  2. Júlio C. Fabris
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  3. Oliver F. Piattella
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  4. Denis C. Rodrigues
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  5. Edison C. O. Santos
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Correspondence to Júlio C. Fabris.

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Bronnikov, K.A., Fabris, J.C., Piattella, O.F. et al. Rastall’s theory of gravity: spherically symmetric solutions and the stability problem. Gen Relativ Gravit 53, 20 (2021). https://doi.org/10.1007/s10714-021-02791-6

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  • DOI: https://doi.org/10.1007/s10714-021-02791-6

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