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Zusammenfassung

Das abschließende Kapitel des zweiten Teils gibt einen kleinen Ausblick auf die Themenkomplexe Gravitationswellen und Kosmologie, die im Rahmen dieses Lehrbuches nicht ausführlich behandelt werden können, sowie auf die große Herausforderung, eine Theorie zu entwickeln, die die ART mit der Quantentheorie zusammenführt. Der Abschnitt über Gravitationswellen beschreibt gesicherte theoretische Erkenntnisse, die auch schon durch astronomische Beobachtungen und experimentelle Messungen bestätigt wurden. Das Gebiet der Kosmologie ist naturgemäß nicht frei von spekulativen Aspekten, wenngleich das sogenannte kosmologische Standardmodell beeindruckende Erfolge vorzuweisen hat. Eine überzeugende Theorie der „Quantengravitation“ gibt es bisher nicht; hier fehlt es noch an empirischen Befunden – und vielleicht auch an einer genialen Idee.

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Literaturverzeichnis

  • Abbott, B. P. et al. [LIGO Scientific Collaboration und Virgo Collaboration] (2016). Observation of gravitational waves from a binary black hole merger. Physical Review Letters 116, 061102.

    Google Scholar 

  • Ablowitz, M.J.,Kaup, D.J.,Newell, A.C., & Segur H. (1974). The inverse scattering transform: Fourier analysis for nonlinear problems. Studies in Applied Mathematics, 53, 249–315.

    Article  MathSciNet  MATH  Google Scholar 

  • Barbour, J., & Pfister, H. (Hrsg.) (1995). Mach’s principle: From Newton’s bucket to quantum gravity. Boston: Birkhäuser.

    MATH  Google Scholar 

  • Bardeen, J.M., & Wagoner R.V. (1971). Relativistic disks: I. Uniform rotation. The Astrophysical Journal, 167, 359–423.

    Article  ADS  MathSciNet  Google Scholar 

  • Belinski, V., & Verdaguer, E. (2001). Gravitational solitons. Cambridge (UK): Cambridge University Press.

    Book  MATH  Google Scholar 

  • Binney, J., & Tremaine, S. (1987). Galactic dynamics. Princeton: Princeton University Press.

    MATH  Google Scholar 

  • Blandford, R.D., & Znajek, R.L. (1977). Electromagnetic extraction of energy from Kerr black holes. Monthly Notices of the Royal Astronomical Society, 179, 433–456.

    Article  ADS  Google Scholar 

  • Bondi, H., & Samuel, J. (1997). The Lense-Thirring effect and Mach’s principle. Physics Letters A, 228, 121–126.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Braginsky, V.B., Polnarev, A.G., & Thorne K.S. (1984). Foucault pendulum at the South Pole: Proposal for an experiment to detect the Earth’s general relativistic gravitomagnetic field. Physical Review Letters, 53, 863–866.

    Article  ADS  Google Scholar 

  • de Broglie, L. (1924). Recherches sur la théorie des quanta (Dissertation). Paris: Masson & Cie.

    Google Scholar 

  • Buchdahl, H.A. (1959). General relativistic fluid spheres. Physical Review, 116, 1027–1034.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Carter, B. (1968). Global structure of the Kerr family of gravitational fields. Physical Review, 174, 1559–1571.

    Article  ADS  MATH  Google Scholar 

  • Carter, B. (1970). The commutation property of a stationary, axisymmetric system. Communications in Mathematical Physics, 17, 233–238.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Carter, B. (1971). Axisymmetric black hole has only two degrees of freedom. Physical Review Letters, 26, 331–333.

    Article  ADS  Google Scholar 

  • Carter, B. (1973). Black hole equilibrium states. In „Black holes“ (herausgegeben von C. DeWitt und B. S. DeWitt) (S. 57–214). New York: Gordon and Breach.

    Google Scholar 

  • Chrusciel, P.T., Costa, J.L., & Heusler, M. (2012). Stationary black holes: Uniqueness and beyond. Living Reviews in Relativity, 15, 7.

    Article  ADS  MATH  Google Scholar 

  • Dirac, P.A.M. (1996). General theory of relativity (Princeton landmarks in physics). Princeton: Princeton University Press. [Erstpublikation: 1975].

    Google Scholar 

  • Droste, J. (1917). The field of a single centre in Einstein’s theory of gravitation, and the motion of a particle in that field. Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, 19, 197–215.

    Google Scholar 

  • Dyson, F.W., Eddington, A.S., & Davidson, C. (1920). A determination of the deflection of light by the Sun’s gravitational field, from observations made at the total eclipse of May 29, 1919. Philosophical Transactions of the Royal Society of London. Series A, 220, 291–333.

    Article  ADS  Google Scholar 

  • Einstein, A. (1915). Zur allgemeinen Relativitätstheorie. Sitzungsberichte der Königlich-Preußischen Akademie der Wissenschaften, 1915, 778–786.

    MATH  Google Scholar 

  • Einstein, A. (1998). The collected papers of Albert Einstein (Bd. 8: The Berlin Years: Correspondence, 1914–1918 (herausgegeben von R. Schulmann et al.)). Dokument 189. Princeton: Princeton University Press.

    Google Scholar 

  • Einstein, A. (2002). The collected papers of Albert Einstein (Bd. 7: The Berlin Years: Writings, 1918–1921 (herausgegeben von M. Janssen et al.)). Dokument 31. Princeton: Princeton University Press.

    Google Scholar 

  • Einstein, A. (2009). Grundzüge der Relativitätstheorie (7. Aufl.). Berlin: Springer. [Erstpublikation: 1922].

    Google Scholar 

  • Ernst, F. (1968a). New formulation of the axially symmetric gravitational field problem. Physical Review, 167, 1175–1177.

    Article  ADS  Google Scholar 

  • Ernst, F. (1968b). New formulation of the axially symmetric gravitational field problem II. Physical Review, 168, 1415–1417.

    Article  ADS  Google Scholar 

  • Friedman, J.L., & Stergioulas N. (2013). Rotating relativistic stars. Cambridge (UK): Cambridge University Press.

    Book  MATH  Google Scholar 

  • Gardner, C.S., Greene, J.M., Kruskal, M.D., & Miura, R.M. (1967). Method for solving the Korteweg-deVries equation. Physical Review Letters, 19, 1095–1097.

    Article  ADS  MATH  Google Scholar 

  • Goenner, H. (1994). Einführung in die Kosmologie. Heidelberg: Spektrum Akademischer Verlag.

    Google Scholar 

  • Göpel, A. (1847). Theoriae transcendentium Abelianarum primi ordinis adumbratio levis. Journal für die reine und angewandte Mathematik, 35, 277–312.

    Article  MathSciNet  Google Scholar 

  • Hartle, J.B. (2003). Gravity: An introduction to Einstein’s general relativity. San Francisco: Addison Wesley.

    Google Scholar 

  • Hawking, S.W., & Ellis, G.F.R. (1973). The large scale structure of space-time. Cambridge (UK): Cambridge University Press.

    Book  MATH  Google Scholar 

  • Hilbert, D. (1915). Die Grundlagen der Physik. Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-physikalische Klasse, 1915, 395–407.

    MATH  Google Scholar 

  • Israel, W. (1968). Event horizons in static electrovac space-times. Communications in Mathematical Physics, 8, 245–260.

    Article  ADS  MathSciNet  Google Scholar 

  • Jacobi, C.G.J. (1832). Considerationes generales de transcendentibus Abelianis. Journal für die reine und angewandte Mathematik, 9, 394–403.

    Article  MathSciNet  Google Scholar 

  • Kerr, R. (1963). Gravitational field of a spinning mass as an example of algebraically special metrics. Physical Review Letters, 11, 237–238.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Kiefer, C. (2012). Quantum gravity (3. Aufl.). Oxford (UK): Oxford University Press.

    MATH  Google Scholar 

  • Killing, W. (1892). Über die Grundlagen der Geometrie. Journal für die reine und angewandte Mathematik, 109, 121–186.

    MathSciNet  MATH  Google Scholar 

  • Komar, A. (1959). Covariant conservation laws in general relativity. Physical Review, 113, 934–936.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Komar, A. (1962). Covariant conservation laws for gravitational radiation. Physical Review, 127, 1411–1418.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Kramer, D., & Neugebauer, G. (1968). Zu axialsymmetrischen stationären Lösungen der Einsteinschen Feldgleichungen für das Vakuum. Communications in Mathematical Physics, 10, 132–139.

    Article  ADS  MathSciNet  Google Scholar 

  • Kramer, M., & Wex, N. (2009). The double pulsar system: A unique laboratory for gravity. Classical and Quantum Gravity, 26, 073001.

    Article  ADS  MATH  Google Scholar 

  • Kundt, W., & Trümper, M. (1966). Orthogonal decomposition of axi-symmetric stationary spacetimes. Zeitschrift für Physik, 192, 419–422.

    Article  ADS  MathSciNet  Google Scholar 

  • Landau, L. D., & Lifschitz, E. M. (1989). Klassische Feldtheorie (Lehrbuch der theoretischen Physik, Bd. II, 11. Aufl.). Berlin: Akademie-Verlag. [Erstpublikation: 1939].

    Google Scholar 

  • Lense, J., & Thirring, H. (1918). Über den Einfluß der Eigenrotation der Zentralkörper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie. Physikalische Zeitschrift, 19, 156–163.

    ADS  MATH  Google Scholar 

  • Lovelock, D. (1971). The Einstein tensor and its generalizations. Journal of Mathematical Physics, 12, 498–501.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Lovelock, D. (1972). The four-dimensionality of space and the Einstein tensor. Journal of Mathematical Physics, 13, 874–876.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Maison, D. (1978). Are the stationary, axially symmetric Einstein equations completely integrable? Physical Review Letters, 41, 521–522.

    Article  ADS  MathSciNet  Google Scholar 

  • Mazur, P.O. (1982). Proof of uniqueness of the Kerr-Newman black hole solution. Journal of Physics A: Mathematical and General, 15, 3173–3180.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Meinel, R. (2012). Constructive proof of the Kerr-Newman black hole uniqueness including the extreme case. Classical and Quantum Gravity, 29, 035004.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Meinel, R. (2016). A physical derivation of the Kerr-Newman black hole solution. Springer Proceedings in Physics, 170, 53–61.

    Google Scholar 

  • Meinel, R., Ansorg, M., Kleinwächter, A., Neugebauer, G., & Petroff, D. (2008). Relativistic figures of equilibrium. Cambridge (UK): Cambridge University Press.

    Book  MATH  Google Scholar 

  • Misner, C.W., Thorne, K.S., & Wheeler, J.A. (1973). Gravitation. New York: W. H. Freeman and Company.

    Google Scholar 

  • Mukhanov, V.F., & Winitzki, S. (2007). Introduction to quantum effects in gravity. Cambridge (UK): Cambridge University Press.

    Book  MATH  Google Scholar 

  • Neugebauer, G. (2000). Rotating bodies as boundary value problems. Annalen der Physik, 9, 342–354.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Neugebauer, G., & Kramer, D. (1969). Eine Methode zur Konstruktion stationärer Einstein-Maxwell-Felder. Annalen der Physik, 24, 62–71.

    Article  ADS  MathSciNet  Google Scholar 

  • Neugebauer G., & Kramer D. (1983). Einstein-Maxwell solitons. Journal of Physics A: Mathematical and General, 16, 1927–1936.

    Article  ADS  MathSciNet  Google Scholar 

  • Neugebauer, G., & Meinel, R. (1993). The Einsteinian gravitational field of the rigidly rotating disk of dust. The Astrophysical Journal, 414, L97–L99.

    Article  ADS  Google Scholar 

  • Neugebauer, G., & Meinel, R. (1994). General relativistic gravitational field of a rigidly rotating disk of dust: Axis potential, disk metric, and surface mass density. Physical Review Letters, 73, 2166–2168.

    Article  ADS  Google Scholar 

  • Neugebauer, G., & Meinel, R. (1995). General relativistic gravitational field of a rigidly rotating disk of dust: Solution in terms of ultraelliptic functions. Physical Review Letters, 75, 3046–3047.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Neugebauer, G., & Meinel, R. (2003). Progress in relativistic gravitational theory using the inverse scattering method. Journal of Mathematical Physics, 44, 3407–3429.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Newman, E.T., Couch, E., Chinnapared, K., Exton, A., Prakash, A., & Torrence, R. (1965). Metric of a rotating, charged mass. Journal of Mathematical Physics, 6, 918–919.

    Article  ADS  MathSciNet  Google Scholar 

  • Novikov, S., Manakov, S.V., Pitaevskii, L.P., & Zakharov, V.E. (1984). Theory of solitons: The inverse scattering method. New York: Consultants Bureau.

    MATH  Google Scholar 

  • Oppenheimer, J.R., & Snyder, H. (1939). On continued gravitational contraction. Physical Review, 56, 455–459.

    Article  ADS  MATH  Google Scholar 

  • Parker, L.E., & Toms, D.J. (2009). Quantum field theory in curved spacetime: Quantized fields and gravity. Cambridge (UK): Cambridge University Press.

    Book  MATH  Google Scholar 

  • Penrose, R. (1969). Gravitational collapse: The role of general relativity. Rivista del Nuovo Cimento, Numero Speziale, I, 252–276.

    ADS  Google Scholar 

  • Pound, R.V., & Rebka, G.A. (1960). Apparent weight of photons. Physical Review Letters, 4, 337–341.

    Article  ADS  Google Scholar 

  • Riemann, B. (1857). Theorie der Abel’schen Functionen. Journal für die reine und angewandte Mathematik, 54, 115–155.

    Article  MathSciNet  Google Scholar 

  • Rindler, W. (2001). Relativity: Special, general, and cosmological. Oxford (UK): Oxford University Press.

    MATH  Google Scholar 

  • Robinson, D.C. (1975). Uniqueness of the Kerr black hole. Physical Review Letters, 34, 905–906.

    Article  ADS  Google Scholar 

  • Rosenhain, G. (1850). Auszug mehrerer Schreiben des Dr. Rosenhain an Herrn Professor Jacobi über die hyperelliptischen Transcendenten. Journal für die reine und angewandte Mathematik, 40, 319–360.

    Article  MathSciNet  Google Scholar 

  • Schwarzschild, K. (1916a). Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie. Sitzungsberichte der Königlich-Preußischen Akademie der Wissenschaften, 1916, 189–196.

    MATH  Google Scholar 

  • Schwarzschild, K. (1916b). Über das Gravitationsfeld einer Kugel aus inkompressibler Flüssigkeit. Sitzungsberichte der Königlich-Preußischen Akademie der Wissenschaften, 1916, 424–434.

    MATH  Google Scholar 

  • Sciama, D. W. (2009). The unity of the universe (Dover science books). Mineola (New York): Dover Publications. [Erstpublikation: 1959].

    Google Scholar 

  • Shapiro, I. I. (1990). Solar system tests of general relativity: Recent results and present plans. In „General Relativity and Gravitation, 1989“ (Proceedings of the 12th International Conference on General Relativity and Gravitation, herausgegeben von N. Ashby et al.) (S. 313–330). Cambridge (UK): Cambridge University Press.

    Google Scholar 

  • Shapiro, S.L., & Teukolsky, S.A. (1983). Black holes, white dwarfs, and neutron stars. New York: John Wiley & Sons.

    Book  Google Scholar 

  • Stephani H. (2004). Relativity: An introduction to special and general relativity. Cambridge (UK): Cambridge University Press.

    Book  Google Scholar 

  • Stephani, H., Kramer, D., MacCallum, M.A.H., Hoenselaers, C., & Herlt, E. (2003). Exact solutions of Einstein’s field equations (2. Aufl.). Cambridge (UK): Cambridge University Press.

    Book  MATH  Google Scholar 

  • Wald, R.M. (1984). General relativity. Chicago: The University of Chicago Press.

    Book  MATH  Google Scholar 

  • Walker, M., & Penrose R. (1970). On quadratic first integrals of the geodesic equations for type {22} spacetimes. Communications in Mathematical Physics, 18, 265–274.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Weierstraß, C. (1854). Zur Theorie der Abelschen Funktionen. Journal für die reine und angewandte Mathematik, 47, 289–306.

    Article  Google Scholar 

  • Weinberg, S. (1972). Gravitation and cosmology: Principles and applications of the general theory of relativity. New York: John Wiley & Sons.

    Google Scholar 

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Meinel, R. (2016). Ausblick. In: Spezielle und allgemeine Relativitätstheorie für Bachelorstudenten. Springer Spektrum, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49856-9_17

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