Annales Henri Poincaré

, Volume 16, Issue 3, pp 801–839 | Cite as

Neutrino Radiation Showing a Christodoulou Memory Effect in General Relativity

  • Lydia BieriEmail author
  • David Garfinkle


We describe neutrino radiation in general relativity by introducing the energy–momentum tensor of a null fluid into the Einstein equations. Investigating the geometry and analysis at null infinity, we prove that a component of the null fluid enlarges the Christodoulou memory effect of gravitational-waves. The description of neutrinos in general relativity as a null fluid can be regarded as a limiting case of a more general description using the massless limit of the Einstein–Vlasov system. Gigantic neutrino bursts occur in our universe in core-collapse supernovae and in the mergers of neutron star binaries.


Neutron Star Fundamental Form Momentum Tensor Gravitational Radiation Spacelike Hypersurface 
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  1. 1.
    Bieri, L.: An extension of the stability theorem of the Minkowski space in general relativity. Ph.D. thesis, ETH Zurich, Zurich (2007)Google Scholar
  2. 2.
    Bieri, L.: Extensions of the Stability Theorem of the Minkowski Space in General Relativity. Solutions of the Einstein Vacuum Equations. AMS-IP, Studies in Advanced Mathematics, Cambridge (2009)Google Scholar
  3. 3.
    Bieri, L.: Spacetimes with Non-isotropic mass in general relativity. Preprint (2013)Google Scholar
  4. 4.
    Bieri, L.: Null fluid coupled to Einstein equations in general relativity. Preprint (2013)Google Scholar
  5. 5.
    Bieri L., Chen P., Yau S.-T.: Null asymptotics of solutions of the Einstein–Maxwell equations in general relativity and gravitational radiation. Adv. Theor. Math. Phys. 15, 4 (2011)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Bieri L., Chen P., Yau S.-T.: The electromagnetic Christodoulou memory effect and its application to neutron star binary mergers. Class. Quantum Gravity 29, 21 (2012)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Bondi H., van der Burg M.G.J., Metzner A.W.K.: Gravitational waves in general relativity. VII. Waves from axi-symmetric isolated systems. Proc. R. Soc. A. 269, 21–52 (1962)CrossRefADSzbMATHMathSciNetGoogle Scholar
  8. 8.
    Braginsky, V.B., Grishchuk, L.P.: Zh. Eksp. Teor. Fiz. 89, 744 (1985). [Sov. Phys. JETP 62, 427 (1986)]Google Scholar
  9. 9.
    Braginsky V.B., Thorne K.S.: Nature (London) 327, 123 (1987)CrossRefADSGoogle Scholar
  10. 10.
    Christodoulou D.: Nonlinear nature of gravitation and gravitational-wave experiments. Phys. Rev. Lett. 67(12), 1486–1489 (1991)CrossRefADSzbMATHMathSciNetGoogle Scholar
  11. 11.
    Christodoulou D., Klainerman S.: The global nonlinear stability of the Minkowski space. In: Princeton Mathematics Series, vol. 41. Princeton University Press, Princeton (1993)Google Scholar
  12. 12.
    Dessart L., Ott C., Burrows A., Rosswog S., Livne E.: Neutrino signatures and the neutrino-driven wind in binary neutron star mergers. ApJ 690, 1681–1705 (2009)CrossRefADSGoogle Scholar
  13. 13.
    Leonor I., Cadonati L., Coccia E., D’Antonio S., Di Credico A., Fafone V., Frey R., Fulgione W., Katsavounidis E., Ott C.D., Pagliaroli G., Scholberg K., Thrane E., Vissani F.: Searching for prompt signatures of nearby core-collapse supernovae by a joint analysis of neutrino and gravitational-wave data. Class. Quantum Gravity 27, 084019 (2010)CrossRefADSGoogle Scholar
  14. 14.
    Müller, B., Janka, H.-T., Marek, A.: A new multi-dimensional general relativistic neutrino hydrodynamics code of core-collapse supernovae III. Gravitational wave signals from supernova explosion models. arXiv:1210.6984v2
  15. 15.
    Ott C.D.: Probing the core-collapse supernova mechanism with gravitational-waves. Class. Quantum Gravity 26, 204015 (2009)CrossRefADSGoogle Scholar
  16. 16.
    Riles K.: Gravitational waves: sources, detectors and searches. Prog. Part. Nucl. Phys. 68, 1–54 (2013)CrossRefADSGoogle Scholar
  17. 17.
    Scholberg K.: Supernova neutrino detection. Ann. Rev. Nucl. Part. Sci. 62, 81–103 (2012)CrossRefADSGoogle Scholar
  18. 18.
    Smith J.R.: The path to the enhanced and advanced LIGO gravitational-wave detectors. Class. Quantum Gravity 26, 114013 (2009)CrossRefADSGoogle Scholar
  19. 19.
    Taylor J.H., Weisberg J.M.: A new test of general relativity—gravitational radiation and the binary pulsar PSR 1913+16. ApJ 253, 908–920 (1982)CrossRefADSGoogle Scholar
  20. 20.
    Zel’dovich, Ya.B., Polnarev, A.G.: Astron. Zh. 51, 30 (1974). [Sov. Astron. 18, 17 (1974)]Google Scholar
  21. 21.
    Zipser, N.: The global nonlinear stability of the trivial solution of the Einstein–Maxwell equations. Ph.D. thesis, Harvard Univ., Cambridge (2000)Google Scholar
  22. 22.
    Zipser, N.: Extensions of the Stability Theorem of the Minkowski Space in General Relativity—Solutions of the Einstein–Maxwell Equations. AMS-IP, Studies in Advanced Mathematics, Cambridge (2009)Google Scholar

Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA
  2. 2.Department of PhysicsOakland UniversityRochesterUSA
  3. 3.Michigan Center for Theoretical Physics, Randall Laboratory of PhysicsUniversity of MichiganAnn ArborUSA

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