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Prog. Theor. Phys. Vol. 112 No. 2 (2004) pp. 241-248

[ Full Text PDF : FREE ACCESS (108K) ]

Euclidean Algorithm for a Gravitational Lens in a Polynomial Equation

Hideki Asada,1,2,* Taketoshi Kasai1 and Masumi Kasai1,**

1 Faculty of Science and Technology, Hirosaki University, Hirosaki 036-8561, Japan
2 GReCO, Institute for Astrophysics at Paris, 98 bis boulevard Arago, 75014 Paris, France

(Received April 7, 2004)

Abstract:

The Euclidean algorithm in algebra is applied to a class of gravitational lenses for which the lens equation consists of any set of coupled polynomial equations in the image position. In general, this algorithm allows us to reduce an apparently coupled system to a single polynomial in one variable (say x in Cartesian coordinates) without the other component (say y), which is expressed as a function of the first component. This reduction enables us to investigate the lensing properties in an algebraic manner: For instance, we can obtain an analytic expression of the caustics by computing the discriminant of the polynomial equation. To illustrate this Euclidean algorithm, we re-examine a binary gravitational lens and show that the lens equation is reduced to a single real fifth-order equation, in agreement with previous works. We apply this algorithm also to the linearlized Kerr lens and find that the lens equation is reduced to a single, real fifth-order one.


URL : http://ptp.ipap.jp/link?PTP/112/241/
DOI : 10.1143/PTP.112.241


*E-mail: asada@phys.hirosaki-u.ac.jp
**E-mail: kasai@phys.hirosaki-u.ac.jp

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See Also:

References:

  1. P. Schneider, J. Ehlers and E. E. Falco, Gravitational Lenses (Springer-Verlag, Berlin, 1992).
  2. H. Asada, Astron. Astrophys. 390 (2002), L11[CrossRef].
  3. H. Asada, T. Hamana and M. Kasai, Astron. Astrophys. 397 (2003), 825[CrossRef].
  4. H. J. Witt, Astron. Astrophys. 236 (1990), 311.
  5. H. J. Witt, Astrophys. J. 403 (1993), 530[CrossRef].
  6. H. Asada, T. Kasai and M. Kasai, Prog. Theor. Phys. 108 (2002), 1031[PTP].
  7. B. L. van der Waerden, Algebra I (Springer, 1966).
  8. H. J. Witt and S. Mao, Astrophys. J. 447 (1995), L105.
  9. N. Dalal, Astrophys. J. 509 (1998), L13[IoP STACKS].
  10. H. Erdl and P. Schneider, Astron. Astrophys. 268 (1993), 453.
  11. H. Asada and M. Kasai, Prog. Theor. Phys. 104 (2000), 95[PTP].
  12. H. Asada, M. Kasai and T. Yamamoto, Phys. Rev. D 67 (2003), 043006[APS].

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