Neutrino trapping in braneworld extremely compact stars

Research Article


Extremely Compact Stars (ECS) contain trapped null geodesics. When such objects enter the evolution period admitting geodetical motion of neutrinos, certain part of neutrinos produced in their interior will be trapped influencing their neutrino luminosity and thermal evolution. We study neutrino trapping in the braneworld ECS, assuming uniform distribution of neutrino emissivity and massless neutrinos. We give the efficiency of the neutrino trapping effects in the framework of the simple model of the internal spacetime with uniform distribution of energy density, and external spacetime described by the Reissner-Nordström geometry characterized by the braneworld “tidal” parameter b. For b < 0 the external spacetime is of the black-hole type, while for b > 0 the external spacetime can be of both black-hole and naked-singularity type. Then the ECS surface radius R can be located also above the unstable (outer) photon circular orbit. Such basically new types of the spacetimes strongly alter the trapping phenomena as compared to the standard case of b = 0. It is shown that the neutrino trapping effects are slightly lowered by the presence of physically more plausible case of b < 0, as compared to the standard internal Schwarzschild spacetime, while they can be magnified by positive tidal charges if b < 1 and lowered for b > 1. However, potential astrophysical relevance of the trapping phenomena is strongly enhanced for negative tidal charges enabling a significant enlargement of the ECS surface radius to values coherent with recent observations.


Neutrino trapping Braneworlds Extremely compact stars 


  1. 1.
    Abdujabbarov A., Ahmedov B.: Test particle motion around a black hole in a braneworld. Phys. Rev. D 81, 044022 (2010)ADSCrossRefGoogle Scholar
  2. 2.
    Abramowicz M.A., Anderson N., Bruni M., Ghosh P., Sonego S.: Gravitational waves from ultracompact stars: the optical geometry view of trapped modes. Class. Quantum Gravity 14, L189–L194 (1997)ADSCrossRefGoogle Scholar
  3. 3.
    Abramowicz M.A., Miller J.C., Stuchlík Z.: Concept of radius of gyration in general relativity. Phys. Rev. D 47, 1440– (1993)ADSCrossRefGoogle Scholar
  4. 4.
    Abramowicz M.A., Prasanna A.R.: Centrifugal force reversal near a Schwarzschild black-hole. Mon. Not. R. Astron. Soc. 245, 720 (1990)ADSGoogle Scholar
  5. 5.
    Aliev A.N., Gümrükçüoğlu A.E.: Charged rotating black holes on a 3-brane. Phys. Rev. D 71, 104027 (2005)MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    Aliev A.N., Talazan P.: Gravitational effects of rotating braneworld black holes. Phys. Rev. D 80, 044023 (2009)MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    Arkani-Hamed N., Dimopoulos S., Dvali G.: The hierarchy problem and new dimensions at a millimeter. Phys. Lett. B 429, 263–272 (1998)ADSCrossRefGoogle Scholar
  8. 8.
    Bahcall S., Lynn B.W., Selipsky S.B.: New models for neutron stars. Astrophys. J. 362, 251–255 (1990)ADSCrossRefGoogle Scholar
  9. 9.
    Böhmer C.G., De Risi G., Harko T., Lobo F.S.N.: Classical tests of general relativity in brane world models. Class. Quantum Gravity 27, 185013 (2010)ADSCrossRefGoogle Scholar
  10. 10.
    Böhmer C.G., Harko T., Lobo F.S.N.: Solar system tests of brane world models. Class. Quantum Gravity 25, 045015 (2008)ADSCrossRefGoogle Scholar
  11. 11.
    Bin-Nun A.Y.: Relativistic images in Randall-Sundrum II braneworld lensing. Phys. Rev. D 81, 123011 (2010)ADSCrossRefGoogle Scholar
  12. 12.
    Bin-Nun A.Y.: Gravitational lensing of stars orbiting Sgr A* as a probe of the black hole metric in the Galactic center. Phys. Rev. D 82, 064009 (2010)ADSCrossRefGoogle Scholar
  13. 13.
    Cottam J., Paerls F., Mendez M.: Gravitationally redshifted absorption lines in the X-ray burst spectra of a neutron star. Nature 420, 51–54 (2002)ADSCrossRefGoogle Scholar
  14. 14.
    Dadhich N., Maartens R., Papadopoulos P., Rezania V.: Black holes on the brane. Phys. Lett. B 487, 1–6 (2000)MathSciNetADSMATHCrossRefGoogle Scholar
  15. 15.
    Dimopoulos S., Landsberg G.: Black holes at the large hadron collider. Phys. Rev. Lett. 87, 161602 (2001)ADSCrossRefGoogle Scholar
  16. 16.
    Germani C., Maartens R.: Stars in the braneworld. Phys. Rev. D 64, 124010 (2001)MathSciNetADSCrossRefGoogle Scholar
  17. 17.
    Glendenning N.K.: First-order phase transitions with more than one conserved charge: consequences for neutron stars. Phys. Rev. D 46, 1274–1287 (1992)ADSCrossRefGoogle Scholar
  18. 18.
    Glendenning N.K.: Compact Stars: Nuclear Physics, Particle Physics, and General Relativity. Springer, New York (2000)MATHGoogle Scholar
  19. 19.
    Haensel P., Zdunik J.L.: A submillisecond pulsar and the equation of state of dense matter. Nature 340, 617–619 (1986)ADSCrossRefGoogle Scholar
  20. 20.
    Hledík, S., Stuchlík, Z., Mrázová, K.: Comparison of general relativistic polytropic and adiabatic fluid spheres with a repulsive cosmological constant. In: Hledík, S., Stuchlík, Z. (eds.) Proceedings of RAGtime 4/5: Workshops on Black Holes and Neutron Stars, Opava, 14–16/13–15 October 2002/03, pp. 75–89. Silesian University in Opava, Opava (2004)Google Scholar
  21. 21.
    Kotrlová A., Stuchlík Z., Török G.: Quasiperiodic oscillations in a strong gravitational field around neutron stars testing braneworld models. Class. Quantum Gravity 25, (2008)ADSCrossRefGoogle Scholar
  22. 22.
    Lattimer J., Prakash M.: The physics of neutron stars. Science 304, 536–542 (2004)ADSCrossRefGoogle Scholar
  23. 23.
    Lattimer J., Prakash M.: Neutron star observations: prognosis on equation of state constraints. Phys. Rep. 442, 109–165 (2007)ADSCrossRefGoogle Scholar
  24. 24.
    Maartens R.: Brane-world gravity. Living Rev. Relativ. 7, 7 (2004)ADSGoogle Scholar
  25. 25.
    Mallick, R., Bhattacharyya, A., Ghosh, S.K., Raha, S.: General relativistic effect on the energy deposition rate for neutrino pair annihilation above the equatorial plane along the symmetry axis near a rotating neutron star. ArXiv e-prints 0905.3605v2 [astro-ph.HE] (2009)Google Scholar
  26. 26.
    Mamadjanov A.I., Hakimov A.A., Tojiev S.R.: Quantum interference effects in spacetime of slowly rotating compact objects in braneworld. Mod. Phys. Lett. A 25, 243–256 (2010)ADSMATHCrossRefGoogle Scholar
  27. 27.
    Miller J., Shahbaz T., Nolan L.A.: Are Q-stars a serious threat for stellar-mass black hole candidates?. Mon. Not. R. Astron. Soc. 294, L25–L29 (1998)ADSCrossRefGoogle Scholar
  28. 28.
    Misner, C.W., Thorne, K.S., Wheeler, J.A.: Gravitation. W. H. Freeman, San Francisco (1973)Google Scholar
  29. 29.
    Morozova V.S., Ahmedov B.J., Abdujabbarov A.A., Mamadjanov A.I.: Plasma magnetosphere of rotating magnetized neutron star in the braneworld. Astrophys. Space Sci. 330, 257–266 (2010)ADSMATHCrossRefGoogle Scholar
  30. 30.
    Nilsson U.S., Ugla C.: General relativistic stars: polytropic equations of state. Ann. Phys. 286, 292–319 (2000)ADSMATHCrossRefGoogle Scholar
  31. 31.
    Østgaard, E.: Internal structure of neutron stars. In: Hledík, S., Stuchlík, Z. (eds.) Proceedings of RAGtime 2/3: Workshops on Black Holes and Neutron Stars, Opava, 11–13/8–10 October 2000/01, pp. 73–102. Silesian University in Opava, Opava (2001)Google Scholar
  32. 32.
    Randall L., Sundrum R.: An alternative to compactification. Phys. Rev. Lett. 83, 4690–4693 (1999)MathSciNetADSMATHCrossRefGoogle Scholar
  33. 33.
    Schee J., Stuchlík Z.: Profiles of emission lines generated by rings orbiting braneworld Kerr black holes. Gen. Relativ. Gravit. 41, 1795– (2009)ADSMATHCrossRefGoogle Scholar
  34. 34.
    Schee J., Stuchlík Z.: Optical phenomena in the field of braneworld Kerr black holes. Int. J. Mod. Phys. D 18, 983– (2009)ADSMATHCrossRefGoogle Scholar
  35. 35.
    Schwarzschild, K.: Über das Gravitationsfeld einer Kugel aus inkompressibler Flüssigkeit nach der Einsteinschen Theorie. Sitzungsber. K. Preuss. Akad. Wiss., Phys.–Math. Kl. 424–434 (1916)Google Scholar
  36. 36.
    Shapiro S.L., Teukolsky S.A.: Black Holes, White Dwarfs and Neutron Stars: The Physics of Compact Objects. Wiley-VCH, New York (1983)CrossRefGoogle Scholar
  37. 37.
    Shiromizu T., Maeda K.-I., Sasaki M.: The Einstein equations on the 3-brane world. Phys. Rev. D 62, 024012 (2000)MathSciNetADSCrossRefGoogle Scholar
  38. 38.
    Stuchlík Z.: Note on the properties of the Schwarzschild-de-Sitter spacetime. Bull. Astronom. Inst. Czechoslov. 41, 341– (1990)ADSGoogle Scholar
  39. 39.
    Stuchlík Z.: Spherically symmetric static configurations of uniform density in spacetimes with a non-zero cosmological constant. Acta Phys. Slovaca 50, 219–228 (2000)Google Scholar
  40. 40.
    Stuchlík Z., Hledík S., Juráň J.: Optical reference geometry of Kerr-Newman spacetimes. Class. Quantum Gravity 17, 2691–2718 (2000)ADSMATHCrossRefGoogle Scholar
  41. 41.
    Stuchlík Z., Hledík S., Šoltés J., Østgaard E.: Null geodesics and embedding diagrams of the interior Schwarzschild–de Sitter spacetimes with uniform density. Phys. Rev. D 64, 044004 (2001)MathSciNetADSCrossRefGoogle Scholar
  42. 42.
    Stuchlík Z., Kotrlová A.: Orbital resonances in discs around braneworld Kerr black holes. Gen. Relativ. Gravit. 41, 1305– (2009)ADSMATHCrossRefGoogle Scholar
  43. 43.
    Stuchlík Z., Schee J.: Appearance of Keplerian discs orbiting Kerr superspinars. Class. Quantum Gravity 27, (2010)ADSCrossRefGoogle Scholar
  44. 44.
    Stuchlík Z., Török G., Hledík S.:, Urbanec, M.: Neutrino trapping in extremely compact objects: I.Efficiency of trapping in the internal Schwarzschild spacetimes.Class. QuantumGravity 26, 035003 (2009)ADSCrossRefGoogle Scholar
  45. 45.
    Weber F.: Pulsars as Astrophysical Laboratories for Nuclear and Particle Physics. Taylor & Francis, London (1999)Google Scholar
  46. 46.
    Weber F., Glendenning N.K.: Application of the improved Hartle method for the construction of general relativistic rotating neutron star models. Astrophys. J. 390, 541 (1992)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Zdeněk Stuchlík
    • 1
  • Jan Hladík
    • 1
  • Martin Urbanec
    • 1
  1. 1.Faculty of Philosophy and Science, Institute of PhysicsSilesian University in OpavaOpavaCzech Republic

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