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.

Automated summary

This study precisely solves the equations of motion of null cosmic strings near black holes in the weak-field approximation, revealing how scattering by black holes transforms string momenta and calculating the corresponding recoil effect and angular momentum change of black holes. The energy of null strings evolves along the null direction of their trajectory, connected with the string optical scalar Z.