Neutron stars in Scalar-Tensor-Vector Gravity

Abstract

Scalar-Tensor-Vector Gravity (STVG), also referred as Modified Gravity (MOG), is an alternative theory of the gravitational interaction. Its weak field approximation has been successfully used to describe Solar System observations, galaxy rotation curves, dynamics of clusters of galaxies, and cosmological data, without the imposition of dark components. The theory was formulated by John Moffat in 2006. In this work, we derive matter-sourced solutions of STVG and construct neutron star models. We aim at exploring STVG predictions about stellar structure in the strong gravity regime. Specifically, we represent spacetime with a static, spherically symmetric manifold, and model the stellar matter content with a perfect fluid energy-momentum tensor. We then derive the modified Tolman–Oppenheimer–Volkoff equation in STVG and integrate it for different equations of state. We find that STVG allows heavier neutron stars than General Relativity (GR). Maximum masses depend on a normalized parameter that quantifies the deviation from GR. The theory exhibits unusual predictions for extreme values of this parameter. We conclude that STVG admits suitable spherically symmetric solutions with matter sources, relevant for stellar structure. Since recent determinations of neutron stars masses violate some GR predictions, STVG appears as a viable candidate for a new gravity theory.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Notes

  1. 1.

    Actually, there is discussion about these statements. For instance, Lasky argued that new generalizations of TeVeS, with equivalent solutions, may solve instability problems (see [16, 17]).

  2. 2.

    Compared to Moffat’s original action at Ref. [11], we nullify the cosmological constant because its effects are negligible over stellar structure, we ignore the scalar field nature of \(\omega \) and set \(\omega =1/\sqrt{12}\), as suggested by Moffat [20, 21], and we set the potential \(W(\phi )=0\) as is usually stated (see Ref. [11]). Also, we propose a slight modification: we change the sign of vector field action \(S_{\phi }\) in order to find agreement with the analogous Einstein–Maxwell formalism.

References

  1. 1.

    Bunge, M.A.: Treatise on Basic Philosophy: Ontology I: The Furniture of the World. Springer, Berlin (1977)

    Book  MATH  Google Scholar 

  2. 2.

    Aprile, E., Alfonsi, M., Arisaka, K., et al.: Dark matter results from 225 live days of XENON100 data. Phys. Rev. Lett. 109, 181301 (2012)

    ADS  Article  Google Scholar 

  3. 3.

    LUX Collaboration: First results from the LUX dark matter experiment at the Sanford Underground Research Facility. ArXiv e-prints: 1310.8214 (2013)

  4. 4.

    Agnese, R., Anderson, A.J., Asai, M., et al.: Search for low-mass weakly interacting massive particles with superCDMS. Phys. Rev. Lett. 112, 241302 (2014)

    ADS  Article  Google Scholar 

  5. 5.

    Milgrom, M.: A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis. Astrophys. J. 270, 365–370 (1983)

    ADS  Article  Google Scholar 

  6. 6.

    Bekenstein, J., Milgrom, M.: Does the missing mass problem signal the breakdown of Newtonian gravity? Astrophys. J. 286, 7–14 (1984)

    ADS  Article  Google Scholar 

  7. 7.

    Sanders, R.H.: Phase coupling gravity and astronomical mass discrepancies. Mon. Not. R. Astron. Soc. 235, 105–121 (1988)

    ADS  Article  Google Scholar 

  8. 8.

    Sanders, R.H.: A stratified framework for scalar–tensor theories of modified dynamics. Astrophys. J. 480, 492–502 (1997)

    ADS  Article  Google Scholar 

  9. 9.

    Bekenstein, J.D.: Relativistic gravitation theory for the modified Newtonian dynamics paradigm. Phys. Rev. D 70, 083509 (2004)

    ADS  Article  Google Scholar 

  10. 10.

    Famaey, B., McGaugh, S.S.: Modified Newtonian dynamics (MOND): observational phenomenology and relativistic extensions. Living Rev. Relativ. 15, 10 (2012)

    ADS  Article  Google Scholar 

  11. 11.

    Moffat, J.W.: Scalar tensor vector gravity theory. J. Cosmol. Astropart. Phys. 3, 4 (2006)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  12. 12.

    Brownstein, J.R., Moffat, J.W.: Galaxy rotation curves without nonbaryonic dark matter. Astrophys. J. 636, 721–741 (2006)

    ADS  Article  Google Scholar 

  13. 13.

    Moffat, J.W., Rahvar, S.: The MOG weak field approximation-II. Observational test of Chandra X-ray clusters. Mon. Not. R. Astron. Soc. 441, 3724–3732 (2014)

    ADS  Article  Google Scholar 

  14. 14.

    Brownstein, J.R., Moffat, J.W.: The bullet cluster 1E0657-558 evidence shows modified gravity in the absence of dark matter. Mon. Not. R. Astron. Soc. 382, 29–47 (2007)

    ADS  Article  Google Scholar 

  15. 15.

    Moffat, J.W., Toth, V.T.: Modified gravity: cosmology without dark matter or Einstein’s cosmological constant.ArXiv e-prints: 0710.0364 (2007)

  16. 16.

    Lasky, P.D.: Black holes and neutron stars in the generalized tensor-vector-scalar theory. Phys. Rev. D 80, 081501 (2009)

    ADS  Article  Google Scholar 

  17. 17.

    Lasky, P.D., Doneva, D.D.: Stability and quasinormal modes of black holes in tensor–vector–scalar theory scalar field perturbations. Phys. Rev. D 82, 124068 (2010)

    ADS  Article  Google Scholar 

  18. 18.

    Mavromatos, N.E., Sakellariadou, M., Yusaf, M.F.: Can the relativistic field theory version of modified Newtonian dynamics avoid dark matter on galactic scales? Phys. Rev. D 79, 081301 (2009)

    ADS  Article  Google Scholar 

  19. 19.

    Seifert, M.D.: Stability of spherically symmetric solutions in modified theories of gravity. Phys. Rev. D 76, 064002 (2007)

    ADS  Article  Google Scholar 

  20. 20.

    Moffat, J.W., Rahvar, S.: The MOG weak field approximation and observational test of galaxy rotation curves. Mon. Not. R. Astron. Soc 436, 1439–1451 (2013)

    ADS  Article  Google Scholar 

  21. 21.

    Moffat, J.W., Toth, V.T.: Fundamental parameter-free solutions in modified gravity. Class. Quantum Gravity 26, 085002 (2009)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  22. 22.

    Moffat, J.W.: Black holes in modified gravity (MOG). Eur. Phys. J. C 75, 175 (2015)

    ADS  Article  Google Scholar 

  23. 23.

    Florides, P.S.: The complete field of charged perfect fluid spheres and of other static spherically symmetric charged distributions. J. Phys. A Math. Gen. 16, 1419 (1983)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  24. 24.

    Maurya, S.K., Gupta, Y.K., Ray, S., Chowdhury, S.R.: Spherically symmetric electromagnetic mass models of embedding class one. ArXiv e-prints: 1506.02498 (2015)

  25. 25.

    Silbar, R.R., Reddy, S.: Neutron stars for undergraduates. Am. J. Phys. 72, 892–905 (2004)

    ADS  Article  Google Scholar 

  26. 26.

    Douchin, F., Haensel, P.: A unified equation of state of dense matter and neutron star structure. Astron. Astrophys. 380, 151–167 (2001)

    ADS  Article  Google Scholar 

  27. 27.

    Pandharipande, V.R., Ravenhall, D.G.: Hot nuclear matter. In: Soyeur, M., Flocard, H., Tamain, B., Porneuf, M. (eds.) NATO Advanced Science Institutes ASI Series B, vol. 205, p. 103. Springer, US (1989)

  28. 28.

    Goriely, S., Chamel, N., Pearson, J.M.: Further explorations of Skyrme–Hartree–Fock–Bogoliubov mass formulas. XII. Stiffness and stability of neutron-star matter. Phys. Rev. C 82, 035804 (2010)

    ADS  Article  Google Scholar 

  29. 29.

    Pearson, J.M., Goriely, S., Chamel, N.: Properties of the outer crust of neutron stars from Hartree–Fock–Bogoliubov mass models. Phys. Rev. C 83, 065810 (2011)

    ADS  Article  Google Scholar 

  30. 30.

    Pearson, J.M., Chamel, N., Goriely, S., Ducoin, C.: Inner crust of neutron stars with mass-fitted Skyrme functionals. Phys. Rev. C 85, 065803 (2012)

    ADS  Article  Google Scholar 

  31. 31.

    Haensel, P., Potekhin, A.Y.: Analytical representations of unified equations of state of neutron-star matter. Astron. Astrophys. 428, 191–197 (2004)

    ADS  Article  MATH  Google Scholar 

  32. 32.

    Potekhin, A.Y., Fantina, A.F., Chamel, N., et al.: Analytical representations of unified equations of state for neutron-star matter. Astron. Astrophys. 560, A48 (2013)

    ADS  Article  Google Scholar 

  33. 33.

    Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T.: Numerical Recipes in FORTRAN 77, vol. 1. Cambridge University Press, Cambridge (1992)

    MATH  Google Scholar 

  34. 34.

    Orellana, M., García, F., Teppa Pannia, F.A., Romero, G.E.: Structure of neutron stars in R-squared gravity. Gen. Relativ. Gravit. 45, 771–783 (2013)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  35. 35.

    Antoniadis, J., Freire, P.C.C., Wex, N., et al.: A massive pulsar in a compact relativistic binary. Science 340, 448 (2013)

    ADS  Article  Google Scholar 

  36. 36.

    Kiziltan, B., Kottas, A., De Yoreo, M., Thorsett, S.E.: The neutron star mass distribution. Astrophys. J. 778, 66 (2013)

    ADS  Article  Google Scholar 

  37. 37.

    Özel, F., Psaltis, D., Narayan, R., Santos Villarreal, A.: On the mass distribution and birth masses of neutron stars. Astrophys. J. 757, 55 (2012)

    ADS  Article  Google Scholar 

  38. 38.

    Demorest, P.B., Pennucci, T., Ransom, S.M., et al.: A two-solar-mass neutron star measured using Shapiro delay. Nature 467, 1081–1083 (2010)

    ADS  Article  Google Scholar 

  39. 39.

    Yazadjiev, S.S., Doneva, D.D., Kokkotas, K.D., Staykov, K.V.: Non-perturbative and self-consistent models of neutron stars in R-squared gravity. J. Cosmol. Astropart. Phys. 6, 3 (2014)

    ADS  Article  Google Scholar 

  40. 40.

    Lasky, P.D., Sotani, H., Giannios, D.: Structure of neutron stars in tensor–vector–scalar theory. Phys. Rev. D 78, 104019 (2008)

    ADS  Article  Google Scholar 

  41. 41.

    Sotani, H.: Slowly rotating relativistic stars in tensor–vector–scalar theory. Phys. Rev. D 81, 084006 (2010)

    ADS  Article  Google Scholar 

  42. 42.

    Yazadjiev, S.S., Doneva, D.D., Kokkotas, K.D.: Rapidly rotating neutron stars in R-squared gravity. Phys. Rev. D 91, 084018 (2015)

    ADS  MathSciNet  Article  Google Scholar 

  43. 43.

    Staykov, K.V., Doneva, D.D., Yazadjiev, S.S., Kokkotas, K.D.: Slowly rotating neutron and strange stars in \(\text{ R }^{2}\) gravity. J. Cosmol. Astropart. Phys. 10, 6 (2014)

    ADS  Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Federico G. Lopez Armengol.

Additional information

This work was supported by Grants PICT 2012-00878 (Agencia Nacional de Promoción Científica y Tecnológica, Argentina) and AYA 2013-47447-C3-1-P (Ministro de Educación, Cultura y Deporte, España). We would like to thank Federico García and Santiago del Palacio for helpful comments.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Lopez Armengol, F.G., Romero, G.E. Neutron stars in Scalar-Tensor-Vector Gravity. Gen Relativ Gravit 49, 27 (2017). https://doi.org/10.1007/s10714-017-2184-0

Download citation

Keywords

  • Modified gravity
  • Vector gravity
  • Neutron stars