Test particle motion in the space-time of a Kerr black hole pierced by a cosmic string

TL;DR

This paper analytically solves the geodesic equations in Kerr black hole spacetime pierced by a cosmic string, revealing how the string influences particle orbits and gravitational effects, with implications for astrophysical observations and cosmic string bounds.

Contribution

It provides the complete analytical solutions for geodesics in a Kerr black hole spacetime with a cosmic string, including effects on orbital dynamics and gravitational phenomena.

Findings

Cosmic string enhances perihelion shift and Lense-Thirring effect.

Upper bound on string energy per unit length from satellite data.

Potential explanation for quasar polarization alignment.

Abstract

We study the geodesic equation in the space-time of a Kerr black hole pierced by an infinitely thin cosmic string and give the complete set of analytical solutions of this equation for massive and massless particles in terms of Mino time that allows to decouple the r- and theta-component of the geodesic equation. The solutions of the geodesic equation can be classified according to the particle's energy and angular momentum, the mass and angular momentum per mass of the black hole. We give examples of orbits showing the influence of the cosmic string. We also discuss the perihelion shift and the Lense-Thirring effect for bound orbits and show that the presence of a cosmic string enhances both effects. Comparing our results with experimental data from the LAGEOS satellites we find an upper bound on the energy per unit length of a string piercing the earth which is approximately 10^{16} kg/m. Our work has also applications to the recently suggested explanation of the alignment of the polarization vector of quasars using remnants of cosmic string decay in the form of primordial magnetic field loops.