Asymptotically simple solutions of the vacuum einstein equations in even dimensions

Communications in Mathematical Physics

Volumn 260, Issue 3, 2005, Pages 557-577

  Anderson, Michael T ^a   Chruściel, Piotr T ^b  

^a STONY BROOK UNIVERSITY   (United States)

^b UNIVERSITÉ DE TOURS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 27244459292     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-005-1424-4     Document Type: Article

References (34)

1. Alinhac, S., Métivier, G.: Propagation de l'analyticité des solutions de systèmes hyperboliques non-linéaires. Invent. Math. 75, 189-204 (1984)
2. Anderson, M.T.: Existence and stability of even dimensional asymptotically de Sitter spaces. http://ar-xiv.org/list, gr-qc/0408072, 2004 (to appear in Annales Henri Poincaré)
3. Andersson, L., Chruściel, P.T.: On "hyperboloidal" Cauchy data for vacuum Einstein equations and obstructions to smoothness of Scri. Commun. Math. Phys. 161, 533-568 (1994)
4. Andersson, L., Moncrief, V.: Elliptic-hyperbolic systems and the Einstein equations. Annales Henri Poincaré 4, 1-34 (2003)
5. Choquet-Bruhat, Y., Geroch, R.: Global aspects of the Cauchy problem in general relativity. Commun. Math. Phys. 14, 329-335 (1969)
6. Choquet-Bruhat, Y., Novelle, M.: Système conforme régulier pour les équations d'Einstein. C. R. Acad. Sci. Paris 205, 155-160 (1987)
7. Choquet-Bruhat, Y., York, J.W.: The Cauchy problem. In: General Relativity and Gravitation - the Einstein Centenary (A. Held, ed.), London-New York: Plenum, 1979, pp. 99-160
8. Chruściel, P.T.: On completeness of orbits of Killing vector fields. Class. Quantum Grav. 10, 2091-2101 (1993)
9. Chruściel, P.T., Delay, E.: Existence of non-trivial asymptotically simple vacuum space-times. Class. Quantum Grav. 19 L71-L79 (2002), erratum-ibid, 3389
10. Chruściel, P.T., Delay, E.: On mapping properties of the general relativistic constraints operator in weighted function spaces, with applications. Mém. Soc. Math. de France. 94, 1-103 (2003)
11. Chruściel, P.T., Lengard, O.: Solutions of wave equations in the radiating regime. Bull. Soc. Math. de France 133, 1-72 (2005)
12. Corvino, J.: Scalar curvature deformation and a gluing construction for the Einstein constraint equations. Commun. Math. Phys. 214, 137-189 (2000)
13. Corvino, J., Schoen, R.: On the asymptotics for the vacuum Einstein constraint equations. http//ar-xiv.org/list/gr-qc/0301071, 2003
14. Dain, S.: Initial data for stationary space-times near space-like infinity. Class. Quantum Grav. 18, 4329-4338 (2001)
15. Damour, T., Schmidt, B.: Reliability of perturbation theory in general relativity. J. Math. Phys. 31, 2441-2453 (1990)
16. Fefferman, C., Graham, C.R.: Conformal invariants. In: Élie Cartan et les mathématiques d'aujourd'hui, The mathematical heritage of Élie Cartan, Sémin. Lyon 1984, Astérisque, No.Hors Sér. 1985, pp. 95-116
17. Fourès-Bruhat, Y.: Théorème d'existence pour certains systèmes d'équations aux dérivées partielles non linéaires. Acta Math. 88, 141-225 (1952)
18. Frauendiener, J.: Some aspects of the numerical treatment of the conformal field equations. In: Proceedings of the Tübingen Workshop on the Conformal Structure of Space-times, H. Friedrich, J. Frauendiener, (eds), Springer Lecture Notes in Physics 604, Berlin-Heidelberg-New York: Springer, 2002, pp. 261-282
19. Friedrich, H.: Conformal Einstein evolution. In: Proceedings of the Tübingen Workshop on the Conformal Structure of Space-times, H. Friedrich, J. Frauendiener, (eds), Springer Lecture Notes in Physics 604, Berlin-Heidelberg-New York: Springer, 2002, pp. 1-50
20. Friedrich, H.: Cauchy problems for the conformal vacuum field equations in general relativity. Commun. Math. Phys. 91, 445-472 (1983)
21. Friedrich, H.: On the existence of n-geodesically complete or future complete solutions of Einstein's field equations with smooth asymptotic structure. Commun. Math. Phys. 107, 587-609 (1986)
22. Friedrich, H.: Einstein equations and conformal structure: existence of anti-de-Sitter-type spacetimes. J. Geom. Phys. 17, 125-184 (1995)
23. Friedrich, H.: Einstein's equation and geometric asymptotics. In: Gravitation and Relativity: at the turn of the Millennium, N. Dahdich, J. Narlikar (eds.), Proceedings of GR15, 1997, Pune, India: IUCAA, 1998, pp. 153-176
24. Geroch, R., Horowitz, G.: Asymptotically simple does notimply asymptotically Minkowskian. Phys. Rev. Lett. 40, 203-206 (1978)
25. Graham, C.R., Hirachi, K.: The ambient obstruction tensor and Q-curvature. (2004) http://ar-vix.org/list/math.DG/0405068v1, 2004
26. Hollands, S., Ishibashi, A.: Asymptotic flatness and Bondi energy in higher dimensional gravity. J. Math. Phys. 46, 022503 (2005)
27. Hollands, S., Wald, R.M.: Conformal null infinity does not exist for radiating solutions in odd spacetime dimensions. Class. Quant. Grav. 21, 5139-5146 (2004)
28. Husa, S.: Numerical relativity with the conformal field equations. In: Proceedings of the Tübingen Workshop on the Conformai Structure of Space-times, H. Friedrich, J. Frauendiener, (eds), Springer Lecture Notes in Physics 604, Berlin-Heidelberg-New York: Springer, 2002, pp. 159-192
29. Kato, T.: The Cauchy problem for quasi-linear symmetric hyperbolic systems. Arch. Rational Mech. Anal. 58, 181-205 (1975)
30. Lengard, O.: Solutions of the Einstein's equation, wave maps, and semilinear waves in the radiation regime, Ph.D. thesis, Université de Tours, 2001, http://www/phys.univ-tours.fr/~piotr/papers/batz, 2001
31. Myers, R.C., Perry, M.J.: Black holes in higher dimensional space-times. Ann. Phys. 172, 304-347 (1986)
32. Schimming, R.: Cauchy's problem for Bach's equations of general relativity. In: Differential geometry (Warsaw, 1979), Banach Center Publ., Vol. 12, Warsaw: PWN, 1984, pp. 225-231
33. Simon, W., Beig, R.: The multipole structure of stationary space-times. Jour. Math. Phys. 24, 1163-1171 (1983)
34. Taylor, M.E.: Partial differential equations. New York, Berlin, Heidelberg: Springer, 1996