Geodesics and geodesic deviation for impulsive gravitational waves

Journal of Mathematical Physics

Volumn 39, Issue 4, 1998, Pages 2201-2212

  Steinbauer, R ^a  

^a UNIVERSITY OF VIENNA   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032369572     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532283     Document Type: Article

References (16)

1. J. Ehlers and W. Kundt, "Exact solutions of the gravitational field equations," in Gravitation, An Introduction to Current Research, edited by L. Witten (Wiley, New York, 1964), pp. 49-99.
2. 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.
3. P. C. Aichelburg and R. U. Sexl, "On the gravitational field of a massless particle," J. Gen. Rel. Grav. 2, 303-312 (1971).
4. H. Balasin and H. Nachbagauer, "The ultrarelativistic Kerr-geometry and its energy-momentum tensor," Class. Quantum Grav. 12, 707-713 (1995).
5. 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).
6. R. Penrose, "Structure of space-time," in Battelle Recontres, edited by C. M. DeWitt and J. A. Wheeler (Benjamin, New York, 1968), pp. 121-235.
7. T. Dray and G. 't Hooft, "The gravitational shockwave of a massless particle," Nucl. Phys. B 232, 173-188 (1985).
8. V. Ferrari, P. Pendenza, and G. Veneziano, "Beam like gravitational waves and their geodesies," J. Gen. Rel. Grav. 20, 1185-1191 (1988).
9. H. Balasin, "Geodesics for impulsive gravitational waves and the multiplication of distributions," Class. Quantum Grav. 14, 455-462 (1997).
10. M. Oberguggenberger, Multiplication of Distributions and Applications to Partial Differential Equations (Longman Scientific and Technical, New York, 1992).
11. R. Steinbauer, "The ultrarelativistic Reissner-Nordstrøm field in the Colombeau algebra," J. Math. Phys. 38, 1614-1622 (1997).
12. O. Hájek, Bull. Am. Math. Soc. 12, 272-279 (1985).
13. J. F. Colombeau, New Generalized Functions and Multiplication of Distributions (North Holland, Amsterdam, 1984).
14. J. F. Colombeau, Multiplication of Distributions (Springer, Berlin, 1992).
15. R. Hermann and M. Oberguggenberger, "Generalized functions, calculus of variations and nonlinear ODEs," preprint (1995).
16. M. Kunzinger, "Lie transformation groups in Colombeau algebras," Ph.D. thesis, University of Vienna, 1996.