Abstract
We consider the point mass and the singular isothermal sphere gravitational lens models in the framework of relativistic theories of gravitation which admit the standard parametrized post-Newtonian (PPN) formalism. In the case of the singular isothermal sphere, we determine the PPN parameter γ in terms of the image angular separation, the ratio of two distances and the velocity dispersion in the deflector which can be evaluated from observations.
REFERENCES
Bekenstein, J. D., and Sanders, R. H. (1994). Astrophys. J. 429, 480.
Gerbal, D., and Sirousse-Zia, H. (1988). Annales de Physique (France) 13, 87.
Pechlaner, E., and Sexl, R. (1966). Commun. Math. Phys. 2, 227.
Bergmann, P. G. (1968). Int. J. Theor. Phys. 1, 25.
Wagoner, R. V. (1970). Phys. Rev. D 1, 3209.
O'Hanlon, J. (1972). Phys. Rev. Lett. 29, 137.
Fujii, Y. (1974). Phys. Rev. D 9, 874.
Fujii, Y. (1975). Gen. Rel. Grav. 6, 29.
Stelle, K. (1978). Gen. Rel. Grav. 9, 353.
Schmidt, H.-J. (1990). Europhys. Lett. 12, 667.
Sanders, R. H. (1984). Astron. Astrophys. 136, L21.
Sanders, R. H. (1986). Astron. Astrophys. 154, 135.
Gerbal, D., and Sirousse-Zia, H. (1989). C. R. Acad. Sci. Paris 309, Série; II, 353.
Sirousse-Zia, H. (1990). Doctorat d'Etat thesis, Université Paris VII.
Sanders, R. H. (1990). Astron. Astrophys. Rev. 2, 1.
Gerhard, O. E., and Spergel, D. N. (1992). Astrophys. J. 397, 38.
Walker, M. (1994). Astrophys. J. 430, 463.
Blandford, R. D., and Kochanek, C. S. (1987). In Dark Matter in the Universe (Proc. 4th Jerusalem Winter School for Theoretical Physics), J. N. Bahcall, T. Piran and S. Weinberg, eds. (World Scientific, Singapore).
Blandford, R., and Narayan, R. (1992). Ann. Rev. Astron. Astrophys. 30, 311.
Schneider, P., Ehlers, J., and Falco, E. E. (1992). Gravitational Lenses (Springer-Verlag, Heidelberg-New York).
Refsdal, S., and Surdej, J. (1994). Rep. Prog. Phys. 56, 117.
Fort, B., and Mellier, Y. (1994). Astron. Astrophys. Rev. 5, 239.
Wu, X. P. (1996). Fund. Cosmic Phys. 17, 1.
Will, C. M. (1993). Theory and Experiment in Gravitational Physics (revised ed., first publ. 1981, Cambridge University Press, Cambridge).
Zwicky, F. (1937). Phys. Rev. 51, 290.
Zwicky, F. (1937). Phys. Rev. 51, 679.
Young, P., Gunn J. E., Kristian, J., Oke, J. B., and Westphal, J. A. (1980). Astrophys. J. 24, 507.
Nottale, L. (1988). In Dark Matter (Moriond Astrophysics Meetings), J. Audouze and J. Tran Thanh Van, eds. (Frontèeres, Gif-sur-Yvette).
Krauss, L. M., and White, M. (1992). Astrophys. J. 397, 357.
Helbig, T. (1991). Astrophys. J. 382, 223.
Vietri, M., and Ostriker, J. P. (1983). Astrophys. J. 267, 488.
Krauss, L. M., and Small, T. A. (1991). Astrophys. J. 378, 22.
Turner, E. L., Ostriker, J. P., and Gott, J. R. (1984). Astrophys. J. 284, 1.
Rights and permissions
About this article
Cite this article
Sirousse-Zia, H. Gravitational Lensing and Relativistic Theories of Gravitation. General Relativity and Gravitation 30, 1273–1280 (1998). https://doi.org/10.1023/A:1026603213696
Issue Date:
DOI: https://doi.org/10.1023/A:1026603213696