Advertisement

General Relativity and Gravitation

, Volume 44, Issue 6, pp 1393–1417 | Cite as

Neutrino trapping in extremely compact objects described by the internal Schwarzschild-(anti-)de Sitter spacetimes

  • Zdeněk Stuchlík
  • Jan Hladík
  • Martin Urbanec
  • Gabriel Török
Research Article

Abstract

Extremely compact stars (ECS) (having radius R < 3GM/c 2) contain captured null geodesics. Certain part of neutrinos produced in their interior will be trapped, influencing thus their neutrino luminosity and thermal evolution. The trapping effect has been previously investigated for the internal Schwarzschild spacetimes with the uniform distribution of energy density. Here, we extend our earlier study considering the influence of the cosmological constant Λ on the trapping phenomena. Our model for the interior of ECS is based on the internal Schwarzschild-(anti-)de Sitter (S(a)dS) spacetimes with uniform distribution of energy density matched to the external vacuum S(a)dS spacetime with the same cosmological constant. Assuming uniform and isotropic distribution of local neutrino emissivity we determine behavior of the trapping coefficients, i.e., “global” one representing influence on the neutrino luminosity and “local” one representing influence on the cooling process. We demonstrate that the repulsive (attractive) cosmological constant has tendency to enhance (damp) the trapping phenomena.

Keywords

Neutrino trapping Extremely compact stars S(a)dS spacetimes 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abdujabbarov A., Ahmedov B.: Test particle motion around a black hole in a braneworld. Phys. Rev. D 81(4), 044022 (2010)ADSCrossRefGoogle Scholar
  2. 2.
    Abramowicz M.A., Andersson N., Bruni M., Ghosh P., Sonego S.: Gravitational waves from ultracompact stars: the optical geometry view of trapped modes. Class. Quantum Gravit. 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, 1440–1447 (1993)ADSCrossRefGoogle Scholar
  4. 4.
    Akmal A., Pandharipande V.R., Ravenhall D.G.: Equation of state of nucleon matter and neutron star structure. Phys. Rev. C 58, 1804–1828 (1998)ADSCrossRefGoogle Scholar
  5. 5.
    Bahcall S., Lynn B.W., Selipsky S.B.: Are neutron stars Q-stars?. Nucl. Phys. B 331, 67–79 (1990)ADSCrossRefGoogle Scholar
  6. 6.
    Bin-Nun A.Y.: Relativistic images in Randall–Sundrum II braneworld lensing. Phys. Rev. D 81(12), 123011 (2010)ADSCrossRefGoogle Scholar
  7. 7.
    Boeckel J., Schaffner-Bielich T.: A little inflation in the early universe at the QCD phase transition. Phys. Rev. Lett. 105(4), 041301 (2010)ADSCrossRefGoogle Scholar
  8. 8.
    Boeckel, T., Schaffner-Bielich, J.: A little inflation at the cosmological QCD phase transition. ArXiv 1105.0832v2 [astro-ph.CO] (2011)Google Scholar
  9. 9.
    Böhmer C.G., Harko T., Lobo F.S.N.: Solar system tests of brane world models. Class. Quantum Gravit. 25(4), 045015 (2008)ADSCrossRefGoogle Scholar
  10. 10.
    Caldwell R.R., Kamionkowski M.: The physics of cosmic acceleration. Annu. Rev. Nucl. Part. Sci. 59, 397–429 (2009)ADSCrossRefGoogle Scholar
  11. 11.
    Dadhich N., Maartens R., Papadopoulos P., Rezania V.: Black holes on the brane. Phys. Lett. B 487, 1–6 (2000)MathSciNetADSMATHCrossRefGoogle Scholar
  12. 12.
    Gandolfi S., Illarionov A.Y., Fantoni S., Miller J.C., Pederiva F., Schmidt K.E.: Microscopic calculation of the equation of state of nuclear matter and neutron star structure. Mon. Not. R. Astron. Soc. 404, L35–L39 (2010)ADSCrossRefGoogle Scholar
  13. 13.
    Germani C., Maartens R.: Stars in the braneworld. Phys. Rev. D 64, 124010 (2001)MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    Glendenning N.K.: Compact Stars: Nuclear Physics, Particle Physics, and General Relativity. Springer, New York (2000)MATHGoogle Scholar
  15. 15.
    Haensel, P., Potekhin, A.Y., Yakovlev, D.G. (eds.): Neutron Stars 1: Equation of State and Structure. Astrophysics and Space Science Library, vol. 326. Springer, New York (2007)Google Scholar
  16. 16.
    Hladík J., Stuchlík Z.: Photon and neutrino redshift in the field of braneworld compact stars. J. Cosmol. Astropart. Phys. 7, 12 (2011)ADSCrossRefGoogle Scholar
  17. 17.
    Horowitz G.T.: Surprising connections between general relativity and condensed matter. Class. Quantum Gravit. 28(11), 114008 (2011)MathSciNetADSCrossRefGoogle Scholar
  18. 18.
    Hubeny, V.E.: Holographic insights and puzzles. ArXiv 1103.1999 [hep-th] (2011)Google Scholar
  19. 19.
    Klähn T., Blaschke D., Typel S., van Dalen E.N.E., Faessler A., Fuchs C., Gaitanos T., Grigorian H., Ho A., Kolomeitsev E.E., Miller M.C., Röpke G., Trümper J., Voskresensky D.N., Weber F., Wolter H.H.: Constraints on the high-density nuclear equation of state from the phenomenology of compact stars and heavy-ion collisions. Phys. Rev. C 74(3), 035802 (2006)ADSCrossRefGoogle Scholar
  20. 20.
    Kološ M., Stuchlík Z.: Current-carrying string loops in black-hole spacetimes with a repulsive cosmological constant. Phys. Rev. D 82(12), 125012 (2010)ADSCrossRefGoogle Scholar
  21. 21.
    Kotrlová A., Stuchlík Z., Török G.: Quasiperiodic oscillations in a strong gravitational field around neutron stars testing braneworld models. Class. Quantum Gravit. 25, 225016 (2008)ADSCrossRefGoogle Scholar
  22. 22.
    Krauss L.M., Turner M.S.: The cosmological constant is back. Gen. Relativ. Gravit. 27, 1137–1144 (1995)ADSMATHCrossRefGoogle Scholar
  23. 23.
    Lattimer J.M., Prakash M.: Neutron star observations: prognosis for equation of state constraints. Phys. Rep. 442, 109–165 (2007)ADSCrossRefGoogle Scholar
  24. 24.
    Linde A.: Particle physics and cosmology. Prog. Theor. Phys. Suppl. 85, 279–292 (1985)ADSCrossRefGoogle Scholar
  25. 25.
    Linde A.D.: Phase transitions in gauge theories and cosmology. Rep. Prog. Phys. 42, 389–437 (1979)ADSCrossRefGoogle Scholar
  26. 26.
    Miller J.C., 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
  27. 27.
    Misner C.W., Thorne K.S., Wheeler J.A.: Gravitation. W.H. Freeman and Co, San Francisco (1973)Google Scholar
  28. 28.
    Morozova V.S., Ahmedov B.J.: Electromagnetic fields of slowly rotating compact magnetized stars in braneworld. Astrophys. Space Sci. 333, 133–142 (2011)ADSMATHCrossRefGoogle 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., Uggla C.: General relativistic stars: polytropic equations of state. Ann. Phys. 286, 292–319 (2000)MathSciNetADSMATHCrossRefGoogle Scholar
  31. 31.
    Østgaard E.: Internal structure of neutron stars. In: Hledík, S., Stuchlík, Z. (eds.) RAGtime 2/3: Workshops on Black Holes and Neutron Stars, pp. 73–102. Silesian University at Opava, Opava (2001)Google Scholar
  32. 32.
    Prikas A.: Q-Stars in anti de Sitter spacetime. Gen. Relativ. Gravit. 36, 1841–1869 (2004)MathSciNetADSMATHCrossRefGoogle Scholar
  33. 33.
    Rhoades C.E., Ruffini R.: Maximum mass of a neutron star. Phys. Rev. Lett. 32, 324–327 (1974)ADSCrossRefGoogle Scholar
  34. 34.
    Rikovska Stone J., Miller J.C., Koncewicz R., Stevenson P.D., Strayer M.R.: Nuclear matter and neutron-star properties calculated with the Skyrme interaction. Phys. Rev. C 68(3), 034324 (2003)ADSCrossRefGoogle Scholar
  35. 35.
    Schee J., Stuchlík Z.: Optical phenomena in the field of braneworld Kerr black holes. Int. J. Mod. Phys. D 18, 983–1024 (2009)ADSMATHCrossRefGoogle Scholar
  36. 36.
    Schee J., Stuchlík Z.: Profiles of emission lines generated by rings orbiting braneworld Kerr black holes. Gen. Relativ. Gravit. 41, 1795–1818 (2009)ADSMATHCrossRefGoogle Scholar
  37. 37.
    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
  38. 38.
    Shapiro S.L., Teukolsky S.A.: Black holes, white dwarfs and neutron stars: the physics of compact objects. Wiley, New York (1983)CrossRefGoogle Scholar
  39. 39.
    Stuchlík Z.: The motion of test particles in black-hole backgrounds with non-zero cosmological constant. Bull. Astron. Inst. Czech. 34, 129–149 (1983)ADSMATHGoogle Scholar
  40. 40.
    Stuchlík Z.: Note on the properties of the Schwarzschild-de-Sitter spacetime. Bull. Astron. Inst. Czech. 41, 341–343 (1990)ADSGoogle Scholar
  41. 41.
    Stuchlík Z.: Spherically symmetric static configurations of uniform density in spacetimes with a non-zero cosmological constant. Acta Phys. Slov. 50, 219–228 (2000)Google Scholar
  42. 42.
    Stuchlík Z.: Influence of the relict cosmological constant on accretion discs. Mod. Phys. Lett. A 20, 561–575 (2005)ADSMATHCrossRefGoogle Scholar
  43. 43.
    Stuchlík Z., Hladík J., Urbanec M.: Neutrino trapping in braneworld extremely compact stars. Gen. Relativ. Gravit. 43, 3163–3190 (2011)ADSMATHCrossRefGoogle Scholar
  44. 44.
    Stuchlík Z., Hledík S.: Some properties of the Schwarzschild-de Sitter and Schwarzschild-anti-de Sitter spacetimes. Phys. Rev. D 60(4), 044006 (1999)MathSciNetADSCrossRefGoogle Scholar
  45. 45.
    Stuchlík Z., Hledík S.: Equatorial photon motion in the Kerr–Newman spacetimes with a non-zero cosmological constant. Class. Quantum Gravit. 17, 4541–4576 (2000)ADSMATHCrossRefGoogle Scholar
  46. 46.
    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(4), 044004 (2001)MathSciNetADSCrossRefGoogle Scholar
  47. 47.
    Stuchlík Z., Kotrlová A.: Orbital resonances in discs around braneworld Kerr black holes. Gen. Relativ. Gravit. 41, 1305–1343 (2009)ADSMATHCrossRefGoogle Scholar
  48. 48.
    Stuchlík Z., Kovář J.: Pseudo-Newtonian gravitational potential for Schwarzschild-de Sitter space-times. Int. J. Mod. Phys. D 17, 2089–2105 (2008)ADSMATHCrossRefGoogle Scholar
  49. 49.
    Stuchlík Z., Schee J.: Influence of the cosmological constant on the motion of Magellanic Clouds in the gravitational field of milky way. J. Cosmol. Astropart. Phys. 9, 18 (2011)ADSCrossRefGoogle Scholar
  50. 50.
    Stuchlík Z., Slaný P., Hledík S.: Equilibrium configurations of perfect fluid orbiting Schwarzschild-de Sitter black holes. Astron. Astrophys. 363, 425–439 (2000)ADSGoogle Scholar
  51. 51.
    Stuchlík Z., Slaný P., Kovář J.: Pseudo-Newtonian and general relativistic barotropic tori in Schwarzschild-de Sitter spacetimes. Class. Quantum Gravit. 26(21), 215013 (2009)ADSCrossRefGoogle Scholar
  52. 52.
    Stuchlík Z., Török G., Hledík S., Urbanec M.: Neutrino trapping in extremely compact objects: I. Efficiency of trapping in the internal Schwarzschild spacetimes. Class. Quantum Gravit. 26, 035003 (2009)ADSCrossRefGoogle Scholar
  53. 53.
    Urbanec M., Běták E., Stuchlík Z.: Observational tests of neutron star relativistic mean field equations of state. Acta Astron. 60, 149–163 (2010)ADSGoogle Scholar
  54. 54.
    Weber F.: Pulsars as astrophysical laboratories for nuclear and particle physics. Taylor & Francis, London (1999)Google Scholar
  55. 55.
    Weber F., Glendenning N.K.: Application of the improved Hartle method for the construction of general relativistic rotating neutron star models. Astrophys. J. 390, 541–549 (1992)ADSCrossRefGoogle Scholar
  56. 56.
    Witten E.: Cosmic separation of phases. Phys. Rev. D 30, 272–285 (1984)MathSciNetADSCrossRefGoogle Scholar
  57. 57.
    Witten E.: The cosmological constant from the viewpoint of string theory. In: Cline, D.B. (ed.) Sources and Detection of Dark Matter and Dark Energy in the Universe, pp. 27. Springer, Berlin (2001)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

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

Personalised recommendations