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Gravitational lensing by cosmic string loops

Gravitational lensing by cosmic string loops. Lagrangian of scalar field :. Euler-Lagrange equation :. Particular solution :. Energy-momentum tensor :. Space-time metric for the case of straight string :. Energy-momentum tensor :. Equations of motion :. Lens equations :.

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Gravitational lensing by cosmic string loops

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  1. Gravitational lensing by cosmic string loops

  2. Lagrangian of scalar field: Euler-Lagrange equation:

  3. Particular solution: Energy-momentum tensor:

  4. Space-time metric for the case of straight string:

  5. Energy-momentum tensor: Equations of motion:

  6. Lens equations:

  7. Magnification of a point source:

  8. Lens equation for circular loop: Magnification of a point source:

  9. Examples of brightness curves for lensing by circular loop.

  10. Lens equations for asymmetric loop: Magnification of a point source:

  11. Caustics (dark), lines of doubling (blue) and loop (red). Critical curves (dark) and loop (red).

  12. Observable data and theoretical curves. Parameters of the loop:

  13. Position ofasymmetric loop at different time.

  14. Lens equations for binary system: Magnification of a point source: Necessary values of system parameters:

  15. Magnification of stars near ends of caustics: Magnification of stars on cusp of caustics:

  16. Loop distribution: Source distribution:

  17. Lensing probability For

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