Abstract
We consider effects due to gravitational lensing by hypothetical cosmic strings. We briefly review facts concerning infinite straight strings, obtain the equation for a gravitational lens produced by an infinite string in the classical form, and analyze features of the gravitational lensing for a given object in detail. We consider a finite straight string. We present caustics and critical curves for strings with different lengths and also some images produced by the considered gravitational lens. We propose a method for constructing brightness curves numerically. As an example of the working capacity of this method, we construct a concrete brightness curve for certain gravitational lens parameters.
Similar content being viewed by others
References
M. R. Anderson, The Mathematical Theory of Cosmic Strings: Cosmic Strings in the Wire Approximation, IOP, Bristol (2003).
A. Vilenkin and E. P. S. Shellard, Cosmic Strings and Other Topological Defects, Cambridge Univ. Press, Cambridge (1994).
B. E. Meierovich, Phys. Usp., 44, 981–997 (2001).
M. Sazhin, G. Longo, M. Capaccioli, J. M. Alcalá, R. Silvotti, G. Covone, O. Khovanskaya, M. Pavlov, M. Pannella, M. Radovich, and V. Testa, Monthly Notice Roy. Astro. Soc., 343, 353–359 (2003); arXiv:astro-ph/0302547v1 (2003).
R. Schild, I. S. Masnyak, B. I. Hnatyk, and V. I. Zhdanov, Astron. Astrophys., 422, 477–482 (2004).
H. Cheng, H. Wang, and J. Man, “The strong field gravitational lensing in the Schwarzschild black hole pierced by a cosmic string,” arXiv:1010.2308v1 [gr-qc] (2010).
P. F. González-Díaz, “Is the 2008 NASA/ESA double Einstein ring actually a ringhole signature?” arXiv: 1001.3778v1 [astro-ph.CO] (2010).
E. Yu. Bannikova and A. T. Kotvytskiy, Monthly Notice Roy. Astro. Soc., 445, 4435–4445 (2014); arXiv: 1410.7946v1 [astro-ph.CO] (2014).
A. T. Kotvyskiy and D. V. Kryuchkov, Vestn. KhNU. Ser. “Fizika”, 1113, No. 20, 63–73 (2014).
A. de Laix and T. Vachaspati, Phys. Rev. D, 54, 4780–4791 (1996); arXiv:astro-ph/9605171v1 (1996).
M. V. Sazhin, O. S. Khovanskaya, M. Capaccioli, G. Longo, M. Paolillo, G. Covone, N. A. Grogin, and E. J. Schreier, Monthly Notice Roy. Astro. Soc., 376, 1731–1739 (2007); arXiv:astro-ph/0611744v2 (2006).
M. V. Sazhin, O. S. Sazhina, M. Capaccioli, G. Longo, M. Paolillo, and G. Riccio, Open Astron. J., 3, 200–206 (2010).
S. V. Krasnikov, Gravit. Cosmol., 15, 62–64 (2009).
P. G. Gavrilenko and L. V. Zadorozhna, Ukr. J. Phys., 54, 319–324 (2009).
K. Kuijken, X. Siemens, and T. Vachaspati, Monthly Notice Roy. Astro. Soc., 384, 161–164 (2008); arXiv:0707.2971v2 [astro-ph] (2007).
S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, Wiley-VCH, eds (1972).
V. G. Levich, Course of Theoretical Physics [in Russian], Vol. 1, Theory of the Electromagnetic Field. Theory of Relativity. Statistical Physics. Electromagnetic Processes in Matter, Fizmatlit, Moscow (1969)
V. G. Levich, English transl: Theoretical Physics, Vol. 1, Theory of the Electromagnetic Field, North-Holland, Amsterdam (1970).
P. Schneider, J. Ehlers, and E. E. Falco, Gravitational Lenses, Springer, Berlin (1999).
A. F. Zakharov, Gravitational Lenses and Microlenses [in Russian], Janus, Moscow (1997).
J. Wambsganss, “Gravitational microlensing,” in: Gravitational Lensing: Strong, Weak, and Micro (Saas- Fee Adv. Courses., Vol. 33, P. Schneider, Ch. Kochanek, and J. Wambsganss, eds.), Springer, Berlin (2006), pp. 453–2.
A. F. Zakharov and M. V. Sazhin, Phys. Usp., 41, 945–982 (1998).
M. V. Sazhin and A. M. Cherepashchuk, Astron. Lett., 20, 523–528 (1994).
S. Mao and B. Paczynski, Astrophys. J. Lett., 374, L37–L40 (1991).
H. Asada, Progr. Theoret. Phys., 110, 425–432 (2003); arXiv:astro-ph/0308280v1 (2003).
C. Alcock, C. W. Akerlof, R. A. Allsman, T. S. Axelrod, D. P. Bennett, S. Chan, K. H. Cook, K. C. Freeman, K. Griest, S. L. Marshall, H. S. Park, S. Perlmutter, B. A. Peterson, M. R. Pratt, P. J. Quinn, A. W. Rodgers, C. W. Stubbs, and W. Sutherland, Nature, 365, 621–623 (1993); arXiv:astro-ph/9309052v1 (1993).
E. Aubourg, P. Bareyre, S. Bréhin, M. Gros, M. Lachiêze-Rey, B. Laurent, E. Lesquoy, C. Magneville, A. Milsztajn, L. Moscoso, F. Queinnec, J. Rich, M. Spiro, L. Vigroux, S. Zylberajch, R. Ansari, F. Cavalier, M. Moniez, J.-P. Beaulieu, R. Ferlet, Ph. Grison, A. Vidal-Madjar, J. Guibert, O. Moreau, F. Tajahmady, E. Maurice, L. Prévôt, and C. Gry, Nature, 365, 623–625 (1993).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 184, No. 1, pp. 160–174, July, 2015.
Rights and permissions
About this article
Cite this article
Kotvytskiy, A.T. Gravitational lensing by straight cosmic strings. Theor Math Phys 184, 1033–1046 (2015). https://doi.org/10.1007/s11232-015-0315-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11232-015-0315-x