A rigorous solution concept for geodesic and geodesic deviation equations in impulsive gravitational waves

Journal of Mathematical Physics

Volumn 40, Issue 3, 1999, Pages 1479-1489

  Kunzinger, M ^a   Steinbauer, R ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033241427     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532816     Document Type: Article

References (24)

1. R. Penrose, "The geometry of impulsive gravitational waves," in General Relativity, Papers in Honour of J. L. Synge, edited by L. O'Raifeartaigh (Clarendon, Oxford, 1972), pp. 101-115.
2. P. C. Aichelburg and R. U. Sexl, "On the gravitational field of a massless particle," Gen. Relativ. Gravit. 2, 303-312 (1971).
3. H. Balasin and H. Nachbagauer, "The ultrarelativistic Kerr-geometry and its energy-momentum tensor," Class. Quantum Grav. 12, 707-713 (1995).
4. C. O. Loustó and N. Sánchez, "The ultrarelativistic limit of the Kerr-Newman geometry and particle scattering at the Planck scale," Phys. Lett. B 232, 462-466 (1989).
5. J. Podolosky and J. B. Griffiths, "Boosted static multipole particles as sources of impulsive gravitational waves," to appear in Phys. Rev. D, gr-qc/9809003 (1998).
6. E. Verlinde and H. Verlinde, "High-energy scattering in Quantum Gravity," Class. Quantum Grav. 10, 175-184 (1993).
7. T. Dray and G. 't Hooft, "The gravitational shockwave of a massless particle," Nucl. Phys. B 232, 173-188 (1985).
8. P. C. Aicheĺburg and H. Balasin, "Generalized symmetries of impulsive gravitational waves," Class. Quantum Grav. 14, A31-A41 (1997).
9. H. Balasin, "Geodesics for impulsive gravitational waves and the multiplication of distributions," Class. Quantum Grav. 14, 455-462 (1997).
10. V. Ferrari, P. Pendenza, and G. Veneziano, "Beam like gravitational waves and their geodesics," Gen. Relativ. Gravit. 20, 1185-1191 (1988).
11. J. Podolsky and K. Vesely, "Continuous coordinates for all impulsive pp-waves," Phys. Lett. A 241, 145-147 (1998).
12. R. Steinbauer, "Geodesics and geodesic deviation for impulsive gravitational waves," J. Math. Phys. 39, 2201-2212 (1998).
13. O. Hájek, Bull. Am. Math. Soc. 12, 272-279 (1985).
14. J. F. Colombeau, New Generalized Functions and Multiplication of Distributions (North Holland, Amsterdam, 1984).
15. J. F. Colombeau, Elementary Introduction to New Generalized Functions (North Holland, Amsterdam, 1985).
16. M. Oberguggenberger, Multiplication of Distributions and Applications to Partial Differential Equations (Longman Scientific and Technical, New York, 1992).
17. R. Hermann and M. Oberguggenberger, "Generalized functions, calculus of variations and nonlinear ODEs," to appear in Nonlinear Theory of Generalized Functions, edited by M. Grosser, G. Hörmann, M. Kunzinger, and M. Oberguggenberger (Pitman Research Notes in Mathematics, 1999).
18. M. Kunzinger, "Lie Transformation Groups in Colombeau Algebras," Ph.D.-thesis, University of Vienna, 1996.
19. J. Podolsky and K. Vesely, "New examples of sandwich gravitational waves and their impulsive limit," Czech. J. Phys. 48, 871 (1998).
20. J. Aragona and H. A. Biagioni, "Intrinsic definition of the Colombeau algebra of generalized functions," Analysis Mathematica 17, 75-132 (1991).
21. C. O. Loustó and N. Sánchez, "Gravitational shock waves generated by extended sources: Ultrarelativistic cosmic strings, monopoles and domain walls," Nucl. Phys. B 355, 231-249 (1991).
22. R. Steinbauer, "The ultrarelativistic Reissner-Nordstrøm field in the Colombeau algebra," J. Math. Phys. 38, 1614-1622 (1997).
23. J. F. Colombeau and A. Meril, "Generalized functions and multiplication of distributions on manifolds," J. Math. Anal. Appl. 186, 357-364 (1994).
24. A. Kriegl and P. W. Michor, The Convenient Setting of Global Analysis (Mathematical Surveys and Monographs Vol. 53 (AMS, Providence, RI, 1997).