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Structure of neutron stars in \(R\)-squared gravity

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Abstract

The effects implied for the structure of compact objects by the modification of General Relativity (GR) produced by the generalization of the Lagrangian density to the form \(f(R)=R+\alpha R^2\), where \(R\) is the Ricci curvature scalar, have been recently explored. It seems likely that this squared-gravity may allow heavier Neutron Stars (NSs) than GR. In addition, these objects can be useful to constrain free parameters of modified-gravity theories. The differences between alternative gravity theories are enhanced in the strong gravitational regime. In this regime, because of the complexity of the field equations, perturbative methods become a good choice to treat the problem. Following previous works in the field, we performed a numerical integration of the structure equations that describe NSs in \(f(R)\)-gravity, recovering their mass-radius relations, but focusing on particular features that arise from this approach in the profiles of the NS interior. We show that these profiles run in correlation with the second-order derivative of the analytic approximation to the Equation of State (EoS), which leads to regions where the enclosed mass decreases with the radius in a counter-intuitive way. We reproduce all computations with a simple polytropic EoS to separate zeroth-order modified gravity effects.

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Notes

  1. The Ricci scalar in terms of the functions of the metric (1) is:

    $$\begin{aligned} R=\frac{2\,e^{-2\Lambda }\!\! \left[r^2 \left\{ \varPhi ^{\prime } \Lambda ^{\prime }+ (\varPhi ^{\prime })^2\!\!+ \varPhi ^{\prime \prime }\!\right\} \!+\!2r\left(\varPhi ^{\prime } - \Lambda ^{\prime }\,\right) -e^{2\Lambda }\!\!+1\right]}{r^2}. \end{aligned}$$

References

  1. Amanullah, R., Lidman, C., Rubin, D., Aldering, G., Astier, P., Barbary, K., Burns, M. S., Conley, A., Dawson, K. S., Deustua, S. E., Doi, M., Fabbro, S., Faccioli, L., Fakhouri, H. K., Folatelli, G., Fruchter, A. S., Furusawa, H., Garavini, G., Goldhaber, G., Goobar, A., Groom, D. E., Hook, I., Howell, D. A., Kashikawa, N., Kim, A. G., Knop, R. A., Kowalski, M., Linder, E., Meyers, J., Morokuma, T., Nobili, S., Nordin, J., Nugent, P. E., Östman, L., Pain, R., Panagia, N., Perlmutter, S., Raux, J., Ruiz-Lapuente, P., Spadafora, A. L., Strovink, M., Suzuki, N., Wang, L., Wood-Vasey, W. M., Yasuda, N., and Supernova Cosmology Project, T.: ApJ 716, 712 (2010)

  2. Arapoğlu, S., Deliduman, C., Yavuz Ekşi, K.: J. Cosmol. Astropart. Phys. 7, 20 (2011)

    Article  ADS  Google Scholar 

  3. Babichev, E., Langlois, D.: Phys. Rev. D 81(12), 124051 (2010)

    Article  ADS  Google Scholar 

  4. Bolejko, K., Célérier, M.-N., Krasiński, A.: Class. Quantum Gravit. 28(16), 164002 (2011)

    Article  ADS  Google Scholar 

  5. Capozziello, S., Faraoni, V.: Beyond Einstein Gravity. A survey of Gravitational Theories for Cosmology and Astrophysics. Springer, Berlin (2011)

    MATH  Google Scholar 

  6. Cooney, A., Dedeo, S., Psaltis, D.: Phys. Rev. D 79(4), 044033 (2009)

    Article  ADS  Google Scholar 

  7. Cooney, A., Dedeo, S., Psaltis, D.: Phys. Rev. D 82(6), 064033 (2010)

    Article  ADS  Google Scholar 

  8. de Felice, A., Tsujikawa, S.: Living Rev. Relativ. 13, 3 (2010)

    ADS  Google Scholar 

  9. DeDeo, S., Psaltis, D.: Phys. Rev. Lett. 90(14), 141101 (2003)

    Article  ADS  Google Scholar 

  10. Deliduman, C., Ekşi, K.Y., Keleş, V.: J. Cosmol. Astropart. Phys. 5, 36 (2011).

    Google Scholar 

  11. Demorest, P.B., Pennucci, T., Ransom, S.M., Roverts, M.S.E, Hesseks, J.W.T: Nature 467, 1081 (2010)

  12. Douchin, F., Haensel, P.: A &A 380, 151 (2001)

    ADS  Google Scholar 

  13. Gungor, C. Yavuz Eksi, K.: ArXiv e-prints /1108.2166 (2011)

  14. Haensel, P., Potekhin, A.Y.: A &A 428, 191 (2004)

    ADS  MATH  Google Scholar 

  15. Hu, W., Sawicki, I.: Phys. Rev. D 76(6), 064004 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  16. Jaime, L.G., Patiño, L., Salgado, M.: Phys. Rev. D 83(2), 024039 (2011)

    Article  ADS  Google Scholar 

  17. Komatsu, E., Smith, K.M., Dunkley, J., Bennett, C.L., Gold, B., Hinshaw, G., Jarosik, N., Larson, D., Nolta, M.R., Page, L., Spergel, D.N., Halpern, M., Hill, R.S., Kogut, A., Limon, M., Meyer, S.S., Odegard, N., Tucker, G.S., Weiland, J.L., Wollack, E., Wright, E.L.: ApJS 192, 18 (2011)

  18. Larson, D., Dunkley, J., Hinshaw, G., Komatsu, E., Nolta, M.R., Bennett, C.L., Gold, B., Halpern, M., Hill, R.S., Jarosik, N., Kogut, A., Limon, M., Meyer, S.S., Odegard, N., Page, L., Smith, K.M., Spergel, D.N., Tucker, G.S., Weiland, J.L., Wollack, E., Wright, E.L.: ApJS 192, 16 (2011)

  19. Miranda, V., Jorás, S.E., Waga, I., Quartin, M.: Phys. Rev. Lett. 102(22), 221101 (2009)

    Article  ADS  Google Scholar 

  20. Oppenheimer, J.R., Volkoff, G.M.: Phys. Rev. 55, 374–381 (1939)

    Google Scholar 

  21. Percival, W.J., Reid, B.A., Eisenstein, D.J., Bahcall, N.A., Budavari, T., Frieman, J.A., Fukugita, M., Gunn, J.E., Ivezić, Ž., Knapp, G.R., Kron, R.G., Loveday, J., Lupton, R.H., McKay, T.A., Meiksin, A., Nichol, R.C., Pope, A.C., Schlegel, D.J., Schneider, D.P., Spergel, D.N., Stoughton, C., Strauss, M.A., Szalay, A.S., Tegmark, M., Vogeley, M.S., Weinberg, D.H., York, D.G., Zehavi, I.: MNRAS 401, 2148 (2010)

    Article  ADS  Google Scholar 

  22. Read, J.S., Lackey, B.D., Owen, B.J., Friedman, J.L.: Phys. Rev. D 79(12), 124032 (2009)

    Article  ADS  Google Scholar 

  23. Riess, A.G., Macri, L., Casertano, S., Sosey, M., Lampeitl, H., Ferguson, H.C., Filippenko, A.V., Jha, S.W., Li, W., Chornock, R., Sarkar, D.: ApJ 699, 539 (2009)

  24. Santos, E.: Phys. Rev. D 81(6), 064030 (2010)

    Article  ADS  Google Scholar 

  25. Santos, E.: AP & SS, 341, 411 (2012)

  26. Silbar, R.R., Reddy, S.: Am. J. Phys. 72, 892 (2004)

    Article  ADS  Google Scholar 

  27. Sotiriou, T.P., Faraoni, V.: Rev. Mod. Phys. 82, 451 (2010)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  28. Starobinsky, A.A.: Sov. J. Exp. Theor. Phys. Lett. 86, 157 (2007)

    Article  ADS  Google Scholar 

  29. Tolman, R.C.: Astrophys. J. 90, 568 (1939)

    Article  ADS  MathSciNet  Google Scholar 

  30. Wen, D.-H., Li, B.-A., Chen, L.-W.: ArXiv e-prints /1101.1504 (2011)

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Acknowledgments

We thank Dr. Arapoğlu for explanations. The authors appreciate helpful comments from Prof. Santiago E. Pérez Bergliaffa. M.O. acknowledge support by the Argentine Agency CONICET and ANPCyT through grants PICT 2010-0213/ Prestamo BID and PICT-2007-00848. G.E.R. was supported by PIP 2010-0078 (CONICET) and the Spanish Ministerio de Innovación y Tecnología under grant AYA 2010-21782-C03-01.

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Authors and Affiliations

  1. Instituto Argentino de Radioastronomía CCT La Plata (CONICET), C.C.5, (1894) Villa Elisa, Buenos Aires, Argentina

    Mariana Orellana, Federico García & Gustavo E. Romero

  2. Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata, Paseo del Bosque s/n 1900, La Plata, Argentina

    Mariana Orellana, Federico García, Florencia A. Teppa Pannia & Gustavo E. Romero

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  1. Mariana Orellana
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  2. Federico García
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  3. Florencia A. Teppa Pannia
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  4. Gustavo E. Romero
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Correspondence to Mariana Orellana.

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Mariana Orellana, Gustavo E. Romero: Member of CONICET.

Federico García, Florencia A. Teppa Pannia: Fellow of CONICET.

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Orellana, M., García, F., Teppa Pannia, F.A. et al. Structure of neutron stars in \(R\)-squared gravity. Gen Relativ Gravit 45, 771–783 (2013). https://doi.org/10.1007/s10714-013-1501-5

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