Nonlinear gravitational waves, their polarization, and realistic sources

Theoretical and Mathematical Physics

Volumn 152, Issue 2, 2007, Pages 1069-1080

  Canfora, F ^a   Parisi, L ^a   Vilasi, G ^a  

^a UNIVERSITY OF SALERNO   (Italy)

Author keywords

Gravitational wave; Killing vector; Metric

Indexed keywords

EID: 34548449438     PISSN: 00405779     EISSN: 15739333     Source Type: Journal    
DOI: 10.1007/s11232-007-0091-3     Document Type: Conference Paper

References (45)

1. V. A. Belinskii and V. E. Zakharov, Soviet Phys. JETP, 48, 985 (1978); 50, 1 (1979).
2. S. De Filippo, G. Marmo, M. Salerno, and G. Vilasi, "On the phase manifold geometry of integrable nonlinear field theory," Preprint IFUSA, Salerno (1982).
3. S. De Filippo, G. Marmo, M. Salerno, and G. Vilasi, Nuovo Cimento B, 83, No. 2, 97 (1984).
4. S. De Filippo, M. Salerno, and G. Vilasi, Lett. Math. Phys., 9, 85 (1985).
5. G. Landi, G. Marmo, and G. Vilasi, J. Math. Phys., 35, 808 (1994).
6. K. S. Thorne, "Gravitational waves," arXiv:gr-qc/9506086v1 (1995).
7. D. Christodoulou, Phys. Rev. Lett., 67, 1486 (1991).
8. K. S. Thorne, Phys. Rev. D, 45, 520 (1992).
9. G. Sparano, G. Vilasi, and A. M. Vinogradov, Phys. Lett. B, 513, 142 (2001).
10. G. Sparano, G. Vilasi, and A. M. Vinogradov, Differential Geom. Appl., 16, 95 (2002).
11. G. Sparano, G. Vilasi, and A. M. Vinogradov, Differential Geom. Appl., 17, 15 (2002).
12. D. Catalano Ferraioli A. M. Vinogradov 2006 Acta Appl. Math. 94 193 D. Catalano Ferraioli and A. M. Vinogradov, Acta Appl. Math., 94, 193 (2006); Preprint DIPS 7/2004, http://diffiety.ac.ru/ (2004).
13. D. Catalano Ferraioli A. M. Vinogradov 2006 Acta Appl. Math. 94 204 D. Catalano Ferraioli and A. M. Vinogradov, Acta Appl. Math., 94, 204 (2006); Preprint DIPS 8/2004, http://diffiety.ac.ru/ (2004).
14. M. Bächtold, "Ricci flat metrics with bidimensional null orbits and non-integrable orthogonal distribution," Preprint DIPS 3/2005, http://diffiety.ac.ru/ (2004).
15. G. Sparano, G. Vilasi, and A. M. Vinogradov, "Einstein metrics with 2-dimensional Killing leaves: III. The semi-integrable case," (to appear).
16. A. Einstein and N. Rosen, J. Franklin Inst., 223, 43 (1937).
17. N. Rosen, Bull. Res. Council Israel, 3, 328 (1954).
18. A. S. Kompaneets, Soviet Phys. JETP, 7, 659 (1958).
19. R. Geroch, J. Math. Phys., 13, 394 (1972).
20. V. A. Belinskii and I. M. Khalatnikov, Soviet Phys. JETP, 30, 1174 (1970).
21. H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers, and E. Herlt, Exact Solutions of Einstein's Field Equations (2nd ed.), Cambridge Univ. Press, Cambridge (2003).
22. F. Canfora and G. Vilasi, Phys. Lett. B, 585, 193 (2004).
23. A. Peres, Phys. Rev. Lett., 3, 571 (1959).
24. A. Peres, Phys. Rev. (2), 118, 1105 (1960).
25. F. Canfora, G. Vilasi, and P. Vitale, Phys. Lett. B, 545, 373 (2002).
26. J. B. Hartle and S. W. Hawking, Phys. Rev. D, 28, 2960 (1983).
27. H. Ooguri and C. Vafa, Nucl. Phys. B, 367, 83 (1991).
28. J. Barret, G. W. Gibbons, M. J. Perry, C. N. Pope, and P. Ruback, Internat. J. Mod. Phys. A, 9, 1457 (1994).
29. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, Wiley, New York (1972).
30. P. A. M. Dirac, General Theory of Relativity, Wiley, New York (1975).
31. F. Canfora, G. Vilasi, and P. Vitale, Internat. J. Mod. Phys. B, 18, 527 (2004).
32. P. C. Aichelburg and R. U. Sexl, Gen. Relativity Gravitation, 2, 303 (1971).
33. E. C. de Rey Neto, Phys. Rev. D, 68, 124013 (2003).
34. V. D. Zakharov, Gravitational Waves in Einstein's Theory, Nauka, Moscow (1972); English transl., Israel Program Sci. Transl., Jerusalem (1973).
35. A. Z. Petrov, Spaces of Einstein, Fizmatgiz, Moscow (1961); English transl.: Einstein Spaces, Pergamon, Oxford (1969).
36. R. Penrose, Ann. Phys., 10, 171 (1960).
37. S. Chandrasekhar, The Mathematical Theory of Black Holes (Int. Ser. Monogr. Phys., Vol. 69), Clarendon Press, Oxford (1983).
38. G. W. Gibbons and P. J. Ruback, Phys. Rev. Lett., 57, 1492 (1986).
39. F. Canfora and G. Vilasi, Class. Q. Grav., 22, 1193 (2005).
40. B. Mashhoon, "Gravitoelectromagnetism," in: Reference Frames and Gravitomagnetism (J.-F. Pascual-Sánchez, I. Floría, A. San Miguel, and F. Vicente, eds.), World Scientific, River Edge, N. J. (2001), p. 121; arXiv:gr-qc/0011014v1 (2000).
41. M. L. Ruggiero and A. Tartaglia, Nuovo Cimento B, 117, 743 (2002).
42. R. A. Hulse and J. H. Taylor, Astrophys. J., 195, L51 (1975).
43. Ya. B. Zel'dovich and I. D. Novikov, Relativistic Astrophysics, Nauka, Moscow (1967); English transl.: Relativistic Astrophysics, Vol. 1, Stars and Relativity, Univ. Chicago Press, Chicago, Ill. (1971).
44. J. Bardeen, Phys. Rev. D, 22, 1882 (1980).
45. T. Battefeld and R. Brandenberger, Phys. Rev. D, 70, 121302(R) (2004).