Kerr-Schild symmetries

General Relativity and Gravitation

Volumn 33, Issue 4, 2001, Pages 649-670

  Coll, Bartolomé ^a   Hildebrandt, Sergi R ^b   Senovilla, José M M ^c  

^a Laboratoire Systemes de Reference Temps Espace   (France)

^b INSTITUT D ESTUDIS ESPACIALS DE CATALUNYA IEEC   (Spain)

^c UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

Author keywords

Space time transformation

Indexed keywords

EID: 0035536452     PISSN: 00017701     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1010265830882     Document Type: Article

References (52)

1. 1. Kerr, R. P., and Schild, A. (1965). In Proceeding of the Galileo Galilei Centenary Meeting on General Relativity, Problems of Energy and Gravitational Waves, G. Barbera, ed., Comiato Nazionale per le Manifestazione Celebrative, Florence, pp. 222-233.
2. 2. Trautman A. (1962). In Recent Developments on General Relativity (Pergamon Press, New York).
3. 3. Kerr, R. P. (1963). Phys. Rev. Lett. 11, 237-238.
4. 4. Kerr, R. P., and Schild A. (1969). Proc. Symp. Appl. Math. 17, 199; Debney, G. C., Kerr, R. P., and Schild A. (1969), J. Math. Phys. 10, 1842-1854; Urbantke, H. (1972), Acta. Phys. Austr. 35, 396; Debney, G. C. (1973), N. Cim. Lett. 8, 337.
5. 4. Kerr, R. P., and Schild A. (1969). Proc. Symp. Appl. Math. 17, 199; Debney, G. C., Kerr, R. P., and Schild A. (1969), J. Math. Phys. 10, 1842-1854; Urbantke, H. (1972), Acta. Phys. Austr. 35, 396; Debney, G. C. (1973), N. Cim. Lett. 8, 337.
6. 4. Kerr, R. P., and Schild A. (1969). Proc. Symp. Appl. Math. 17, 199; Debney, G. C., Kerr, R. P., and Schild A. (1969), J. Math. Phys. 10, 1842-1854; Urbantke, H. (1972), Acta. Phys. Austr. 35, 396; Debney, G. C. (1973), N. Cim. Lett. 8, 337.
7. 4. Kerr, R. P., and Schild A. (1969). Proc. Symp. Appl. Math. 17, 199; Debney, G. C., Kerr, R. P., and Schild A. (1969), J. Math. Phys. 10, 1842-1854; Urbantke, H. (1972), Acta. Phys. Austr. 35, 396; Debney, G. C. (1973), N. Cim. Lett. 8, 337.
8. 5. Vaidya, P. C. (1972). Tensor N.S. 24, 315-321; Debney, G. C. (1974), J. Math. Phys. 15, 992-997; Bhatt, P. V., and Vaidya, S. K. (1991), Class. Quantum Grav. 8, 1717-1722.
9. 5. Vaidya, P. C. (1972). Tensor N.S. 24, 315-321; Debney, G. C. (1974), J. Math. Phys. 15, 992-997; Bhatt, P. V., and Vaidya, S. K. (1991), Class. Quantum Grav. 8, 1717-1722.
10. 5. Vaidya, P. C. (1972). Tensor N.S. 24, 315-321; Debney, G. C. (1974), J. Math. Phys. 15, 992-997; Bhatt, P. V., and Vaidya, S. K. (1991), Class. Quantum Grav. 8, 1717-1722.
11. 6. Vaidya, P. C. (1973) Tensor N.S. 27, 276-280; Urbantke, H. (1975), Acta Phys. Austr. 41, 1: Herlt, E. (1980) Gen. Rel. Grav. 12, 1-7.
12. 6. Vaidya, P. C. (1973) Tensor N.S. 27, 276-280; Urbantke, H. (1975), Acta Phys. Austr. 41, 1: Herlt, E. (1980) Gen. Rel. Grav. 12, 1-7.
13. 6. Vaidya, P. C. (1973) Tensor N.S. 27, 276-280; Urbantke, H. (1975), Acta Phys. Austr. 41, 1: Herlt, E. (1980) Gen. Rel. Grav. 12, 1-7.
14. 7. Mas, L. (1969) C.R. Acad. Sci. Paris A 268, 441-444; (1970), Ph.D. Thesis, Universitat Autònoma de Barcelona; Debney G. C. (1972), Tensor N.S. 24, 227-230; Gürses, M. and Gürsey, F. (1975), J. Math. Phys. 16, 2385-2390; Kerr, R. P., and Wilson, W. B. (1979), Gen. Rel. Grav. 10, 273-281.
15. 7. Mas, L. (1969) C.R. Acad. Sci. Paris A 268, 441-444; (1970), Ph.D. Thesis, Universitat Autònoma de Barcelona; Debney G. C. (1972), Tensor N.S. 24, 227-230; Gürses, M. and Gürsey, F. (1975), J. Math. Phys. 16, 2385-2390; Kerr, R. P., and Wilson, W. B. (1979), Gen. Rel. Grav. 10, 273-281.
16. 7. Mas, L. (1969) C.R. Acad. Sci. Paris A 268, 441-444; (1970), Ph.D. Thesis, Universitat Autònoma de Barcelona; Debney G. C. (1972), Tensor N.S. 24, 227-230; Gürses, M. and Gürsey, F. (1975), J. Math. Phys. 16, 2385-2390; Kerr, R. P., and Wilson, W. B. (1979), Gen. Rel. Grav. 10, 273-281.
17. 7. Mas, L. (1969) C.R. Acad. Sci. Paris A 268, 441-444; (1970), Ph.D. Thesis, Universitat Autònoma de Barcelona; Debney G. C. (1972), Tensor N.S. 24, 227-230; Gürses, M. and Gürsey, F. (1975), J. Math. Phys. 16, 2385-2390; Kerr, R. P., and Wilson, W. B. (1979), Gen. Rel. Grav. 10, 273-281.
18. 7. Mas, L. (1969) C.R. Acad. Sci. Paris A 268, 441-444; (1970), Ph.D. Thesis, Universitat Autònoma de Barcelona; Debney G. C. (1972), Tensor N.S. 24, 227-230; Gürses, M. and Gürsey, F. (1975), J. Math. Phys. 16, 2385-2390; Kerr, R. P., and Wilson, W. B. (1979), Gen. Rel. Grav. 10, 273-281.
19. 8. Kramer, D., Stephani, H., Herlt, E., and MacCallum, M. A. H. (1980). Exact Solutions of Einstein's Field Equations (Cambridge University Press, Cambridge).
20. 9. Thompson, A. H. (1966). Tensor N.S. 17, 92-95.
21. 10. Taub, A. H. (1981). Ann. Phys. (NY) 134, 326-372.
22. 11. Bilge, A. K., and Gürses, M. (1982). In "XI International Colloquiam on Group Theoretical Methods in Physics", M. Cerdaroglu and E. Inönü, (Springer Verlag, Istanbul), pp. 252-255; (1986), J. Math. Phys. 27, 1819-1833.
23. 11. Bilge, A. K., and Gürses, M. (1982). In "XI International Colloquiam on Group Theoretical Methods in Physics", M. Cerdaroglu and E. Inönü, (Springer Verlag, Istanbul), pp. 252-255; (1986), J. Math. Phys. 27, 1819-1833.
24. 12. Nahmad-Achar, E. (1988). J. Math. Phys. 29, 1879-1884.
25. 13. Coll, B., (1999). In Relativity and Gravitation in General. Proceedings of the Spanish Relativity Meeting in Honour of the 65th Birthday of L. Bel, J. Martin, E. Ruiz, F. Atrio, and A. Molina, eds. (World Scientitic, Singapore), pp. 91-98.
26. 14. Talbot, C. J. (1969). Commun. Math. Phys. 13, 45-61; Mastronikola, K. E. (1987), Class. Quantum Grav. 4, L179-L184; Kupeli, A. H. (1988), Class Quantum Grav. 5, 401-408; Fels, M., and Held, A. (1989), Gen. Rel. Grav. 21, 61-68.
27. 14. Talbot, C. J. (1969). Commun. Math. Phys. 13, 45-61; Mastronikola, K. E. (1987), Class. Quantum Grav. 4, L179-L184; Kupeli, A. H. (1988), Class Quantum Grav. 5, 401-408; Fels, M., and Held, A. (1989), Gen. Rel. Grav. 21, 61-68.
28. 14. Talbot, C. J. (1969). Commun. Math. Phys. 13, 45-61; Mastronikola, K. E. (1987), Class. Quantum Grav. 4, L179-L184; Kupeli, A. H. (1988), Class Quantum Grav. 5, 401-408; Fels, M., and Held, A. (1989), Gen. Rel. Grav. 21, 61-68.
29. 14. Talbot, C. J. (1969). Commun. Math. Phys. 13, 45-61; Mastronikola, K. E. (1987), Class. Quantum Grav. 4, L179-L184; Kupeli, A. H. (1988), Class Quantum Grav. 5, 401-408; Fels, M., and Held, A. (1989), Gen. Rel. Grav. 21, 61-68.
30. 15. Martín, J., and Senovilla, J. M. M., (1986). J. Math. Phys. 27, 265-270 (erratum p. 2209); Senovilla, J. M. M., (1987), Class Quantum Grav. 4, 1449-1455; Martin-Pascual, F., and Senovilla, J. M. M. (1988), J. Math. Phys. 29, 937-944; Senovilla, J. M. M., and Sopuerta, C. F. (1994), Class. Quantum Grav. 11, 2073-2083.
31. 15. Martín, J., and Senovilla, J. M. M., (1986). J. Math. Phys. 27, 265-270 (erratum p. 2209); Senovilla, J. M. M., (1987), Class Quantum Grav. 4, 1449-1455; Martin-Pascual, F., and Senovilla, J. M. M. (1988), J. Math. Phys. 29, 937-944; Senovilla, J. M. M., and Sopuerta, C. F. (1994), Class. Quantum Grav. 11, 2073-2083.
32. 15. Martín, J., and Senovilla, J. M. M., (1986). J. Math. Phys. 27, 265-270 (erratum p. 2209); Senovilla, J. M. M., (1987), Class Quantum Grav. 4, 1449-1455; Martin-Pascual, F., and Senovilla, J. M. M. (1988), J. Math. Phys. 29, 937-944; Senovilla, J. M. M., and Sopuerta, C. F. (1994), Class. Quantum Grav. 11, 2073-2083.
33. 15. Martín, J., and Senovilla, J. M. M., (1986). J. Math. Phys. 27, 265-270 (erratum p. 2209); Senovilla, J. M. M., (1987), Class Quantum Grav. 4, 1449-1455; Martin-Pascual, F., and Senovilla, J. M. M. (1988), J. Math. Phys. 29, 937-944; Senovilla, J. M. M., and Sopuerta, C. F. (1994), Class. Quantum Grav. 11, 2073-2083.
34. 16. Magli, G. (1995). J. Math. Phys. 36, 5877-5896; Udeschini, B., and Magli, G. (1996), J. Math. Phys. 37, 5695-5714.
35. 16. Magli, G. (1995). J. Math. Phys. 36, 5877-5896; Udeschini, B., and Magli, G. (1996), J. Math. Phys. 37, 5695-5714.
36. 17. Gergely, L. Å., and Perjés, Z. (1993). Phys. Lett. A 181, 345-348; (1994), J. Math. Phys. 35, 2438-2447, 2448-2462.
37. 17. Gergely, L. Å., and Perjés, Z. (1993). Phys. Lett. A 181, 345-348; (1994), J. Math. Phys. 35, 2438-2447, 2448-2462.
38. 18. Xanthopoulos, B. C. (1978). J. Math. Phys. 19, 1607-1609; Mastronikola, K. E. (1987), Class. Quantum Grav. 4, L179-L184; Mastronikola, K. E., and Xanthopoulos, B. C. (1989), Class. Quantum Grav. 6, 1613-1626.
39. 18. Xanthopoulos, B. C. (1978). J. Math. Phys. 19, 1607-1609; Mastronikola, K. E. (1987), Class. Quantum Grav. 4, L179-L184; Mastronikola, K. E., and Xanthopoulos, B. C. (1989), Class. Quantum Grav. 6, 1613-1626.
40. 18. Xanthopoulos, B. C. (1978). J. Math. Phys. 19, 1607-1609; Mastronikola, K. E. (1987), Class. Quantum Grav. 4, L179-L184; Mastronikola, K. E., and Xanthopoulos, B. C. (1989), Class. Quantum Grav. 6, 1613-1626.
41. 19. All our geometrical considerations being local, it has to be understood that transformations and groups of transformations are both local. In fact, without ad hoc global assumptions on the space-time, one cannot ensure the existence of global transformations, and consequently, one can only infere the existence of possible pseudogroups on the whole manifold.
42. 20. Riemannian and Symplectic manifolds show that strict or conformal invariance of symmetric and antisymmetric regular tensors is respectively finite and infinite dimensional. It is interesting to observe that the non-homogeneous character of the equations in the Kerr-Schild case is responsible for the possibility of having infinite dimensions, despite the symmetry and the regular character of the tensor g involved.
43. 21. Penrose, R., and Rindler, W. (1984). Spinors and Space time (Cambridge University Press, Cambridge).
44. 22. Papadopoulos, A. D. (1983). Tensor N.S. 40, 135-143; (1985). Tensor N.S. 42, 90-92.
45. 22. Papadopoulos, A. D. (1983). Tensor N.S. 40, 135-143; (1985). Tensor N.S. 42, 90-92.
46. 23. Schouten, J. A. (1954). Ricci Calculus (Springer-Verlag, Berlin).
47. 24. Katzin, G. H., Levine, J., and Davis, W. R. (1969). J. Math. Phys. 10, 617.
48. 25. Ehlers, J., and Kundt, W. (1962). in Gravitation: An Introduction to Current Research, ed. L. Witten (Wiley, New York.)
49. 26. Vaidya, P. C. (1951). Proc. Indian Acad. Sci. A 33, 264; (1953), Nature 171, 260.
50. 26. Vaidya, P. C. (1951). Proc. Indian Acad. Sci. A 33, 264; (1953), Nature 171, 260.
51. 27. Defrise-Carter L. (1975). Commun. Math. Phys. 40, 273-282.
52. 28. Hildebrandt, S. R., (2000). Preprint.