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Relativistic images : ウィキペディア英語版
Relativistic images

Relativistic images are images of gravitational lensing which result due to light deflections by angles \hat > 3 \pi/2.
This term was coined by Virbhadra and Ellis〔K. S. Virbhadra and G. F. R. Ellis, ''Phys. Rev.'' D62, 084003 (2000).
〕 in the year 2000 and is used by many researchers working in this field〔Examples:

*A. Y. Bin-Nun, ''Phys. Rev.'' D 81, 123011 (2010);
*O. Yu. Tsupko and G. S. Bisnovatyi-Kogan, ''Gravitation and Cosmology'', 15, 184 (2009);
*E. F. Eiroa, G. E. Romero, and D. F. Torres, ''Phys. Rev.'' D66, 024010 (2002);
*T. Kanti Dey, S. Sen, Mod. ''Phys. Lett.'' A23, 953 (2008);
*E. F. Eiroa, ''Phys. Rev.'' D71, 083010 (2005);
*V. Bozza, ''Phys. Rev.'' D67, 103006 (2003);
*A. Bhadra, ''Phys.Rev.'' D67 (2003) 103009;
*K. Sarkar, A. Bhadra, ''Class. Quant. Grav.'' 23 (2006) 6101;
*Y. Liu, S. Chen, Jiliang Jing, ''Phys. Rev.'' D81:124017, 2010;
*G. N. Gyulchev, S. S. Yazadjiev, ''Phys. Rev.'' D75, 023006,(2007);
*S. Chen, J.Jing ''Phys. Rev.'' D80, 024036, (2009);
*G. N. Gyulchev, S. S. Yazadjiev, ''Phys. Rev.'' D78, 083004, (2008);
*A.O. Petters, ''Mon. Not .Roy. Astron. Soc.'' 338 (2003) 457;
*A. S. Majumdar, N. Mukherjee, ''Int. J. Mod. Phys.'' D14 (2005) 1095;
*M. Sereno, ''Phys.Rev.'' D69 (2004) 023002;
*I. Zh. Stefanov, S. S. Yazadjiev, G. G. Gyulchev, arXiv:1003.1609v2 ();
*N. Mukherjee, A. S. Majumdar, ''Gen. Rel. Grav.'' 39, 583, (2007);
*Clarissa-Marie Claudel, K.S. Virbhadra, and G. F. R. Ellis, ''J. Math. Phys.'' 42, 818-838 (2001)
*K. S. Virbhadra and G. F. R. Ellis, ''Phys. Rev.'' D65, 103004 (2002); K. S. Virbhadra, ''Phys. Rev.'' D79, 083004 (2009;)
*T. Ghosh, S. Sengupta, ''Phys. Rev.'' D81, 044013,2010;
*R. Whisker, ''Phys. Rev.'' D71 (2005) 064004;
*S. Rahvar, A. Mehrabi, M. Dominik, arXiv:1008.1033v1 ();
*C. Leiva, J. Saavedra, J. Villanueva, ''Mod. Phys. Lett.'' A24, 1443, (2009);
*R. Sosnovskiy, arXiv:0806.4379v4 ();
*C. R. Keeton, A. O. Petters, ''Phys. Rev.'' D73 (2006) 044024;
*K. K. Nandi, Yuan-Zhong Zhang, Alexander V. Zakharov, ''Phys. Rev.'' D74 (2006) 024020;
*M. Sereno, F. De Luca, ''Phys. Rev.'' D78, 023008, (2008);
*F. De Paolis, A. Geralico, G. Ingrosso, A.A. Nucita, A. Qadir, ''Astron. Astrophys.'' 415 (2004) 1;
*C. Stornaiolo, ''Gen. Rel. Grav.'' 34 (2002) 2089;
*C.R. Keeton, A. O. Petters, ''Phys. Rev.'' D72 (2005) 104006;
*T. Harko, Z. Kovács, Francisco S. N. Lobo, arXiv:0908.2874v1 ();
*M. Sereno, ''Phys. Rev.'' D78, 083003,(2008);
*M. Sereno, ''Phys. Rev.'' D77, 043004,(2008);
*S. V. Iyer and A. O. Petters, ''Gen. Rel. Grav.'' 39, 1563,(2007);
*T. Harko, Z. Kovács, F. S. N. Lobo, ''Phys. Rev.'' D80, 044021, (2009);
*M. Sereno, ''Mon. Not. Roy. Astron. Soc.'' 344, 942 2003;
*C. G. Boehmer, T. Harko, ''Class. Quant. Grav.'' 24, 3191,(2007);
*A. N. Aliev, P. Talazan, ''Phys. Rev.'' D80, 044023 (2009);
*V. Perlick, arXiv:0708.0178v1 ();
*V. Bozza, arXiv:0911.2187v2 ().〕
(see also in , , and .)
They further defined a term ''relativistic Einstein rings''.〔
==Relativistic Einstein rings==
Relativistic Einstein rings are ringed shaped images occurring due to light deflection \hat>2 \pi when the light source, the lens (the deflector), and the observer are perfectly aligned.
Obviously, ''relativistic Einstein rings'' are ''relativistic images'' for the case when the source, lens, and observer are aligned. Relativistic images are very much demagnified and are extremely difficult to observe due to their poor magnifications as well as some additional problems.

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