Skip to main content

Nonlinear Wave Propagation in Relativistic Hydrodynamics and Cosmology

  • Chapter
General Relativity and Gravitation

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 9))

Abstract

Relativistic nonlinear wave propagation plays an important role in various areas of relativistic astrophysics and cosmology.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Anile, A.M.: 1978, “Non-linear high-frequency waves in relativistic cosmology”, Atti Accad. Naz. Lincei, Rend. Ci. Sci. Fis. Mat. Nat., 63, 375.

    Google Scholar 

  • Anile, A.M.: 1983a, “A geometric characterization of the compatibility relations for regularly discontinuous tensor field”, to be published in Le Matematiche.

    Google Scholar 

  • Anile, A.M.: 1983b, “Evolution of shock waves in relativistic continuum mechanics”, to be published in Ann. Inst. Henri Poincaré.

    Google Scholar 

  • Anile, A.M.: 1983c, “Propagation of weak shocks in relativistic fluid dynamics”, to be published in the Proceedings of the “Journées rélativistes”, Turin.

    Google Scholar 

  • Anile, A.M. and Greco, A.: 1978, “Asymptotic waves and critical time in general relativistic magneto-hydrodynamics”, Ann. Inst. Henri Poincaré, 29,257.

    MathSciNet  ADS  MATH  Google Scholar 

  • Anile, A.M. and Greco, A.: 1979a, “Shock formation and shock structure in the cosmological radiative era”, Lett. Nuovo Cimento, 26, 121.

    Article  ADS  Google Scholar 

  • Anile, A.M. and Greco, A.: 1979b, “Non-linear wave propagation in a proton-electron plasma coupled with a strong radiation field”, Nuovo Cimento, 54, 307.

    Article  MathSciNet  Google Scholar 

  • Anile, A.M. and Majorana, A.: 1981, “Shock structure for heat conducting and viscid fluids”, Meccanica, 2, 149.

    Article  ADS  Google Scholar 

  • Anile, A.M., Miller, J.C. and Motta, S.: 1980, “Damping of relativistic shocks, in annekpanding universe”, Lett. Nuovo Cimento, 29, 268.

    Article  ADS  Google Scholar 

  • Anile, A.M., Miller, J.C. and Motta, S.: 1983, “Formation and damping of relativistic strong shocks”, Phys. Fluids, 26, 1450.

    Article  ADS  MATH  Google Scholar 

  • Anile, A.M. and Muscato, O.: 1983, “Simple waves in relativistic magnetofluiddynamics”, to be published in Lett. Nuovo Cimento.

    Google Scholar 

  • Bampi, F. and Morro, A.: 1980, “Two approaches to non-stationary relativistic thermodynamics”, J. Math. Phys., 21, 1201.

    Article  MathSciNet  ADS  Google Scholar 

  • Barrow, J.: 1980, “Galaxy formation: the first million years”, Philos. Trans. R. Soc. London, A296, 273.

    Article  ADS  Google Scholar 

  • Blandford, R.D. and McKee, C.F.: 1976, “Fluid dynamics of relativistic blast waves”, Phys. Fluids, 19, 1130.

    Article  ADS  MATH  Google Scholar 

  • Bogoyavlenskii, O.I.: 1977, “General relativistic self-similar solution with a spherical shock wave”, Sov. Phys. JETP, 46, 633.

    MathSciNet  ADS  Google Scholar 

  • Boillat, G.: 1965, La propagation des ondes, Gauthier-Villars, Paris.

    MATH  Google Scholar 

  • Boillat, G.: 1975, “Chocs caractéristiques et ondes simple exceptionelles pour les systèmes conservatifs à intégrale d’énergie: forme explicite de la solutions”, C.R. Seances Acad. Sci. Paris, 280A, 1325.

    MathSciNet  Google Scholar 

  • Boillat, G.: 1982, “Urti”, in Ferrarese (ed.), Wave propagation , Liguori, Napoli.

    Google Scholar 

  • Cahill, M.E. and Taub, A.H.: 1971, “Spherically symmetric similarity solutions of the Einstein field equations for a perfect fluid”, Commun. Math. Phys., 21, 1.

    Article  MathSciNet  ADS  Google Scholar 

  • Cattaneo, C.: 1948, “Sulla conduzione del calore”, Atti Semin. Mat. Fis. Univ. Modena, 3, 83.

    MathSciNet  Google Scholar 

  • Chapline, G.F. and Weaver, T.A.: 1979, “Structure of relativistic shock waves in simple gases”, Phys. Fluids, 22, 1885.

    Article  ADS  Google Scholar 

  • Chen, P.J.: 1976, Selected topics in wave propagation, Noordhoff, Leyden.

    MATH  Google Scholar 

  • Chevalier, R.A.: 1981, “Hydrodynamic models of supernova explosions”, Fundamentals of cosmic physics, 7, 1.

    ADS  Google Scholar 

  • Choquet-Bruhat, Y.: 1969, “Ondes asymptotiques et approchées pour des systèmes d’équations aux dérivées partielles non linéaires”, J. Math. Pures et Appl., 48, 117.

    MathSciNet  MATH  Google Scholar 

  • Choquet-Bruhat, Y.: 1982, “Ondes asymptotiques”, in Ferrarese (ed.), Wave propagation, Liguori, Napoli.

    Google Scholar 

  • De Groot, S.R., Vande Leeuwen, W.A. and Van Weert, Ch.G.: 1980, Relativistio kinetic theory, North Holland, Amsterdam.

    Google Scholar 

  • Dixon, G.: 1978, Special Relativity, the foundation of macroscopic physics, Cambridge University Press, Cambridge.

    MATH  Google Scholar 

  • Eckhoff, K.: 1981, “On stability for symmetric hyperbolic systems, I”, J. Differ. Equations, 40, 94.

    Article  MathSciNet  MATH  Google Scholar 

  • Friedlander, F.G.: 1975, The wave equation on a curved space-time, Cambridge University Press, Cambridge.

    MATH  Google Scholar 

  • Gilbard, D. and Paolucci, D.: 1953, “The structure of shock waves in the continuum theory of fluids”, J. Rat. Mech. An., 2, 617.

    Google Scholar 

  • Gross, R.A.: 1971, “The physics of strong shock waves in gases”, in P. Caldirola and H. Knoepfel, (ed.), Physics of High Energy density, Academic Press Inc., New York.

    Google Scholar 

  • Ikeuchi, S., Tomisaka, K. and Ostriker, J.: 1983, “The structure and expansion law of a shock wave in an expanding universe”, Astrophys. J., 265, 583.

    Article  MathSciNet  ADS  Google Scholar 

  • Israel, W.: 1976, “Nonstationary irreversible thermodynamics: a causal relativistic theory”, Ann. Rhys. (USA), 100, 310.

    Article  MathSciNet  ADS  Google Scholar 

  • Israel, W. and Stewart, J.: 1979, “On transient relativistic thermodynamics and kinetic theory”, Rroc. R. Soc., London, A365, 43.

    Article  MathSciNet  ADS  Google Scholar 

  • Jeffrey, A.: 1976, Quasilinear hyperbolic systems and waves, Pitman, London.

    MATH  Google Scholar 

  • Jones, B.J.T.: 1971, “The origin and evolution of structure in the Universe”, unpublished Ph. D. Thesis, Cambridge.

    Google Scholar 

  • Jones, B.J.T.: 1976, “The origin of galaxies: A review of recent theoretical developments and their confrontation with observation”, Rev. Mod. Phys., 48, 107.

    Article  ADS  Google Scholar 

  • Kline, M. and Kay, I.: 1965, Electromagnetic theory and Geometrical Optics, J. Wiley and Sons, New York.

    MATH  Google Scholar 

  • Koch, P.A.: 1965, “Relativistic shock structure”, Phys. Rev., A140, 1161.

    Article  ADS  Google Scholar 

  • Lanza, A., Miller, J.C. and Motta, S.: 1982, “Relativistic shocks in a Synge gas”, Lett. Nuovo Cimento, 35, 309.

    Article  ADS  Google Scholar 

  • Landau, L.D. and Lifshitz, E.M.: 1959, Fluid Mechanics, Pergamon Press, London.

    Google Scholar 

  • Lanza, A., Miller, J.C. and Motta, S.: 1983, “Relativistic shock waves in a Synge gas”, preprint, University of Catania.

    Google Scholar 

  • Liang, E.P.T.: 1977a, “Relativistic simple waves: shock damping and entropy production”, Astrophys. J., 211, 361.

    Article  ADS  Google Scholar 

  • Liang, E.P.T.: 1977b, “Galaxies and entropy from nonlinear fluctuations: a simple waves analysis”, Astrophys. J., 216, 206.

    Article  ADS  Google Scholar 

  • Liang, E.P.T. and Baker, K.: 1977, “Damping of relativistic shocks”, Phys. Rev. Lett., 39, 191.

    Article  ADS  Google Scholar 

  • Lichnerowicz, A.: 1971, “Ondes de choc, ondes infinitésimales et rayons en hydrodynamique et magneto-hydrodynamique relativistes”, in C. Cattaneo (éd.), Relativistic fluid dynamics, Cremonese, Roma.

    Google Scholar 

  • Lichnerowicz, A.: 1975, “Ondes de choc gravitationelles et ondes de choc mangétomatérielles extrêmes”, C.R. Seances Acad. Sci. Paris, 281, 929.

    MathSciNet  ADS  MATH  Google Scholar 

  • Lindblom, L. and Hiscock, A.A.: 1983, “On the stability of rotating stellar models in general relativity theory”, Astrophys. J., 267, 384.

    Article  MathSciNet  ADS  Google Scholar 

  • Ludwig, D.: 1966, “Uniform asymptotic expansion at a caustic”, Commun. Pure Appl. Math., 19, 215.

    Article  MathSciNet  MATH  Google Scholar 

  • MacCallum, M.A.H., and Taub, A.H.: 1973, “The averaged lagrangian and high-frequency gravitational waves”, Commun. Math. Phys., 30, 153.

    Article  MathSciNet  ADS  Google Scholar 

  • Maugin, G.: 1976, “Conditions de compatibilité pour une hypersurface singulière en mécanique relativiste des milieux continus”, Ann. Inst. Henri Poincaré, 24, 213.

    MathSciNet  MATH  Google Scholar 

  • Modugno, M. and Stefani, G.: 1979, “On the geometrical structure of shock waves in general relativity”, Ann. Inst. Henri Poincaré, 30, 27.

    MathSciNet  ADS  MATH  Google Scholar 

  • Müller, I.: 1967, “Zum Paradoxon der Wärmeleitungstheorie”, Z. Phys., 198, 329.

    Article  ADS  MATH  Google Scholar 

  • Müller, I. and Liu, I.: 1983, “Extended thermodynamics of classical and degenerate ideal gases”, preprint, University of Berlin.

    Google Scholar 

  • Peebles, P.J.E.: 1970, “Non linear limit on primeval adiabatic perturbations”, Phys. Rev., D1, 397.

    ADS  Google Scholar 

  • Peebles, P.J.E.: 1980, The large-scale structure of the universe, Princeton University Press, Princeton.

    Google Scholar 

  • Ruggeri, T. and Strumia, A.: 1981, “Main field and convex covariant density for quasi-linear hyperbolic systems”, Ann. Inst. Henri Poincaré, 34, 65.

    MathSciNet  MATH  Google Scholar 

  • Schmidt, B.: 1964, “Electron beam density measurement in shock waves in argon”, J. Fluid Mech., 39,361.

    Article  ADS  Google Scholar 

  • Serrin, P.: 1959, “Mathematical principles of Classical fluid mechanics”, in Handbuck der Physik, VIII/1, Springer-Verlag, New York.

    Google Scholar 

  • Taub, A.H.: 1948, “Relativistic Rankine-Hugoniot equations”, Phys. Rev.,74, 328.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Taub, A.H.: 1978, “Relativistic fluid mechanics”, Annu. Rev. Fluid Mech., 10, 301.

    Article  MathSciNet  ADS  Google Scholar 

  • Taussig, R.: 1973, “Shock wave production of relativistic plasmas”, in M.J. Lighthill, I. Imai and H. Sato (eds), Dynamics of ionized gases, University of Tokyo Press, Tokyo.

    Google Scholar 

  • Van Riper, K.A.: 1979, “General relativistic hydrodynamics and the adiabatic collapse of stellar cores”, Astrophys. J.,232, 558.

    Article  ADS  Google Scholar 

  • Vishniac, E.T.: 1982, “Nonlinear effects on cosmological perturbations. I. The evolution of adiabatic perturbations”, Astrophys. J., 253, 446.

    Article  MathSciNet  ADS  Google Scholar 

  • Whitham, G.B.: 1974, Linear and nonlinear waves, J. Wiley and Sons, New York.

    Google Scholar 

  • Zeldovich, Y.B. and Novikov, I.D.s 1982, Struttura ed evoluzione dell’Universo, (Italian edition), Editori Riuniti, Roma.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1984 D. Reidel Publishing Company

About this chapter

Cite this chapter

Anile, A.M. (1984). Nonlinear Wave Propagation in Relativistic Hydrodynamics and Cosmology. In: Bertotti, B., de Felice, F., Pascolini, A. (eds) General Relativity and Gravitation. Fundamental Theories of Physics, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6469-3_16

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-6469-3_16

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-6471-6

  • Online ISBN: 978-94-009-6469-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics