1. VISIBLE PROPERTIES OF COSMIC ANTI-STRING Kotvytskiy A.T., Shulga V.M. Institute of Radio Astronomy of Nat. Ac. Sci. of Ukraine Karazin Kharkov National University, Ukraine

2. GRAVITATIONAL LENS EQUATION FOR A STRAIGHT COSMIC STRING - indicates the source; - shows a light ray that crosses the lens plane; - is observer; - are the distances. - is linear energy density; Source of light which is situated in the plane of source Straight cosmic string that lies in the lens plane

3. GRAVITATIONAL LENS EQUATION FOR A STRAIGHT COSMIC STRING In the case of an arbitrary string lying in the lens plane for deflection angle we have formula is vector point to the string from the string center of mass, is parameter along the string. For straight string of length L which is situated symmetrically along the axis the formula for deflection angle have type

4. GRAVITATIONAL LENS EQUATION FOR A STRAIGHT COSMIC STRING After an elementary integration, we obtain the components of the deflection angle We approach L to infinity and depending on the sign of we obtain:

5. GRAVITATIONAL LENS EQUATION FOR A STRAIGHT COSMIC STRING Simple gravitational lens configuration For small angles and for geometrically-thin lenses

6. GRAVITATIONAL LENS EQUATION FOR A STRAIGHT COSMIC STRING Dimensionless variables Lens equation Cut angle This leads to the fact that if the source is in the sector cut by angle double alpha, then the observer sees two images located symmetrically with respect to the actual position of the source. Thus, we find that in the case of an infinity straight string we have cut angle delta theta that equals double alpha (deficit angle) 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).

7. GRAVITATIONAL LENS EQUATION FOR A STRAIGHT COSMIC STRING The straight string lies in the lens plane along the axis and then the lens equation can be rewritten in terms of the following components This approach lets us easily turn from a string with positive energy density to a string with negative energy density. where

8. GRAVITATIONAL LENS EQUATION FOR A STRAIGHT COSMIC ANTI -STRING is negative and we introduce new parameter alpha with tilde. Then, the equation changes to the following type This system has other properties comparing to the previous case.

9. GRAVITATIONAL LENS EQUATION FOR A STRAIGHT COSMIC ANTI -STRING The image does not exist coordinate of the source coordinate of the image

10. GRAVITATIONAL LENS EQUATION FOR A STRAIGHT COSMIC ANTI -STRING coordinate of the source

11. Anti-string String COMPARE GRAVITATIONAL LENSING ON COSMIC STRING AND ANTI-STRING

12. Anti-string String COMPARE GRAVITATIONAL LENSING ON COSMIC STRING AND ANTI-STRING

13. Anti-string String COMPARE GRAVITATIONAL LENSING ON COSMIC STRING AND ANTI-STRING

14. Anti-string String COMPARE GRAVITATIONAL LENSING ON COSMIC STRING AND ANTI-STRING

15. The magnification factor on anti-string with parameter MICROLENSING EFFECT solid curve dotted curve dash-and-dot curve

16. WEAK LENSING The sources – red points Varying anti-string parameter from to The images – blue points

17. WEAK LENSING if the images density near the string goes up if the images density is equal everywhere if the images density near the string goes down

18. CONCLUSION If in our Universe exist objects with negative mass or negative energy density, we can discover them with proper observations by their specific visible properties. Thank you