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Lorentzian Manifolds

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Quantum Field Theory on Curved Spacetimes

Part of the book series: Lecture Notes in Physics ((LNP,volume 786))

Abstract

In this chapter some basic notions from Lorentzian geometry will be reviewed. In particular causality relations will be explained, Cauchy hypersurfaces and the concept of global hyperbolic manifolds will be introduced. Finally the structure of globally hyperbolic manifolds will be discussed. More comprehensive introductions can be found in [1] and [2].

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References

  1. O’Neill, B.: Semi-Riemannian Geometry. Academic Press, San Diego (1983)

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  2. Wald, R.M.: General Relativity. University of Chicago Press, Chicago (1984)

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  3. Bär, C., Ginoux, N., Pfäffle, F.: Wave equations on Lorentzian manifolds and quantization. EMS Publishing House, Zürich (2007)

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  4. Friedlander, F.: The wave equation on a curved space-time. Cambridge University Press, Cambridge (1975)

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  5. Leray, J.: Hyperbolic Differential Equations. Mimeographed Lecture Notes, Princeton (1953)

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  6. Bernal, A.N., Sánchez, M.: Smoothness of time functions and the metric splitting of globally hyperbolic spacetimes. Commun. Math. Phys. 257, 43 (2005)

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  7. Geroch, R.: Domain of dependence. J. Math. Phys. 11, 437 (1970)

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  8. Ellis, G.F.R., Hawking, S.W.: The large scale structure of space-time. Cambridge University Press, London-New York (1973)

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  9. Bernal, A.N., Sánchez, M.: Further results on the smoothability of Cauchy hypersurfaces and Cauchy time functions. Lett. Math. Phys. 77, 183 (2006)

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Correspondence to Frank Pfäffle .

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Pfäffle, F. (2009). Lorentzian Manifolds. In: Bär, C., Fredenhagen, K. (eds) Quantum Field Theory on Curved Spacetimes. Lecture Notes in Physics, vol 786. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02780-2_2

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  • DOI: https://doi.org/10.1007/978-3-642-02780-2_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02779-6

  • Online ISBN: 978-3-642-02780-2

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