Wave Equation and Causality Violation

Alain Bachelot

Séminaire Équations aux dérivées partielles (2001-2002)

  • Volume: 2001-2002, page 1-13

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Bachelot, Alain. "Wave Equation and Causality Violation." Séminaire Équations aux dérivées partielles 2001-2002 (2001-2002): 1-13. <http://eudml.org/doc/11049>.

@article{Bachelot2001-2002,
author = {Bachelot, Alain},
journal = {Séminaire Équations aux dérivées partielles},
language = {eng},
pages = {1-13},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Wave Equation and Causality Violation},
url = {http://eudml.org/doc/11049},
volume = {2001-2002},
year = {2001-2002},
}

TY - JOUR
AU - Bachelot, Alain
TI - Wave Equation and Causality Violation
JO - Séminaire Équations aux dérivées partielles
PY - 2001-2002
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2001-2002
SP - 1
EP - 13
LA - eng
UR - http://eudml.org/doc/11049
ER -

References

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  1. A. Bachelot. Global properties of the wave equation on non-globally hyperbolic manifolds. J. Math. Pures Appl., 81: 35–65, 2002. Zbl1078.58016MR1994882
  2. A. Bachelot, A. Motet-Bachelot. Les résonances d’un trou noir de Schwarzschild. Ann. Inst. Henri Poincaré - Physique théorique, 59(1): 3–68, 1993. Zbl0793.53094
  3. M.  Beals, M. Reed. Microlocal regularity theorems for nonsmooth pseudodifferential operators and applications to nonlinear problems. Trans. Amer. Math. Soc., 285(1): 159–184, 1984. Zbl0562.35093MR748836
  4. J-M.  Bony. Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires. Ann. Sci. École Norm. Sup., 14(2): 209–246, 1981. Zbl0495.35024MR631751
  5. Y.  Bruhat. Sur la théorie des propagateurs. Ann. di Mat. Pura Appl., 64: 191–228, 1964. Zbl0173.36501MR169659
  6. Y.  Choquet-Bruhat. Hyperbolic partial differential equations on a manifold. Battelle Rencontres, 1967, Benjamin, New York, 84–106, 1968. Zbl0169.43202MR239299
  7. D.  Colton, R. Kress. Inverse Acoustic and Electromagnetic Scattering Theory. Springer-Verlag, second edition 1998. Zbl0760.35053MR1635980
  8. J.  Cooper, W. Strauss. Representations of the Scattering Operator for Moving Obstacles. Indiana Univ. Math. J., 28(4): 643–671, 1979. Zbl0427.35056MR542950
  9. S.  Deser, R. Jackiw, G. ’t Hooft. Three dimensional Einstein gravity: Dynamics of flat space. Ann. Phys. (NY), 152: 220–235, 1984. 
  10. Y.  Fourès, I.E. Segal. Causality and analyticity. Trans. Am. Math. Soc., 78: 385–405, 1955. Zbl0064.36805MR69401
  11. F. G.  Friedlander. The wave equation on a curved space-time. Cambridge University Press, 1975. Zbl0316.53021MR460898
  12. J. L.  Friedman, M.S. Morris. Existence and Uniqueness Theorems for Massless Fields on a Class of Spacetimes with Closed Timelike Curves. Commun. Math. Phys., 186: 495–529, 1997. Zbl0965.83028MR1463811
  13. R. P.  Geroch. The domain of dependence. J. Math. Phys., 11: 437–449, 1970. Zbl0189.27602MR270697
  14. G. W.  Gibbons, C.A.R. Herdeiro. Supersymmetric rotating black holes and causality violation. Class. Quantum Grav., 16: 3619–3652, 1999. Zbl0956.83050MR1729962
  15. K.  Gödel. An example of a new type of cosmological solution of Einstein’s field equations of gravitation. Rev. Mod. Phys., 21: 447–450, 1949. Zbl0041.56701
  16. D.  Häfner. Complétude asymptotique pour l’équation des ondes dans une classe d’espaces-temps stationnaires et asymptotiquement plats. Ann. Institut Fourier, 51(3): 779–833, 2001. Zbl0981.35031
  17. S. W.  Hawking. Chronology protection conjecture. Phys. Rev. D, 46(2): 603–611, 1992. MR1172250
  18. S. W.  Hawking, G. F. R. Ellis. The large scale structure of space-time. Cambridge University Press, 1974. Zbl0265.53054MR424186
  19. L.  Hörmander. The Analysis of Linear Partial Differential Operators, I, II, III, IV. Springer Verlag, second printing 1994. MR1996773
  20. L.  Hörmander. A Remark on the Characteristic Cauchy Problem. J. Funct. Anal., 93: 270–277, 1990. Zbl0724.35060MR1073287
  21. T.  Ikebe. A Spectral Theory for the reduced Wave Equation with a Complex Refractive Index. Publ. RIMS, Kyoto Univ., 8: 579–606, 1972/73. Zbl0261.35066MR326185
  22. T. Kato. Perturbation Theory for Linear Operators. Springer Verlag, second edition, 1980. Zbl0148.12601MR407617
  23. B. S..  Kay. Application of linear hyperbolic PDE to linear quantum fields incurved spacetimes: especially black holes, time machines and a new semi-local vacuum concept. Journées Equations aux dérivées partielles, Exposé IX, Nantes, 2000. Zbl1011.81046MR1775685
  24. R. P.  Kerr. Gravitational field of a spinning mass as an example of algebraically special metrics. Phys. Rev. Lett., 11: 237–238, 1963. Zbl0112.21904MR156674
  25. P.  Lax, R. Phillips. Scattering Theory. Academic Press, Revised Edition 1989. Zbl0186.16301MR1037774
  26. J.  Leray. Hyperbolic differential equations. Princeton University, 1952. Zbl0588.35002MR80849
  27. J-L.  Lions, E. Magenes. Problèmes aux limites non homogènes et applications I. Dunod, 1968. Zbl0165.10801
  28. R. B.  Melrose. Geometric Scattering Theory. Cambridge University Press, 1995. Zbl0849.58071MR1350074
  29. A.  Papapetrou. Champs gravitationnels à symétrie axiale. Ann. Inst. Henri Poincaré, A4: 83–105, 1966. Zbl0118.23002
  30. V.  Petkov. Scattering Theory for Hyperbolic Operators. North Holland, 1989. Zbl0687.35067MR1028780
  31. M. Reed, B. Simon. The Scattering of Classical Waves from Inhomogeneous Media. Math. Z., 155: 163–180, 1977. Zbl0338.35073MR481641
  32. M. Reed, B. Simon. Methods of modern mathematical physics, Vol. II, III, IV. Academic Press, 1975, 1978. Zbl0308.47002MR493422
  33. W. J.  van Stockum. Gravitational field of a distribution of particles rotating about an axis of symetry. Proc. R. Soc. Edin., 57: 135–154, 1937. Zbl0016.28302
  34. F. J.  Tipler. Singularities and Causality Violation. Ann. Phys., 108: 1–36, 1977. Zbl0369.53057MR471924
  35. B. R.  Vainberg. Asymptotic Methods in Equations of Mathematical Physics. Gordon and Breach Science Publishers, 1989. Zbl0743.35001MR1054376
  36. M.  Visser. Lorentzian Wormholes. Springer Verlag, 1995. MR1348164
  37. M.  Zworski. Poisson formulae for resonances. Séminaire E.D.P., Ecole Polytechnique, Exposé XIII, 1996–1997. Zbl1255.35084MR1482819

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