Null cosmic strings: Scattering by black holes, optics, and spacetime content

Equations of motion of null cosmic strings near black holes, or other massive sources, are solved exactly in the weak-field approximation. The stress-energy tensor of a null string in a curved spacetime is introduced and used to show how scattering by black holes transforms linear and angular momenta of the string. The corresponding recoil effect of a black hole and change of its angular momentum caused by a null cosmic string are calculated. For a null string, its energy ?? per unit length evolves along the null direction of the string trajectory. The evolution of ?? is connected with a string optical scalar Z. Optical properties of null strings are that their energy is concentrated on caustics, where Z has poles. String parameters ?? and Z capture important features of the spacetime where strings move. Explicit dependence of ?? and Z on the strain and Bondi news tensors of gravitational wave background, mass and angular momentum aspects are established, near the future-null infinity, up to the fourth order in expansion in an inverse null parameter in asymptotically flat spacetimes.