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Test particle motion in the space-time of a Kerr black hole pierced by a cosmic string
General Relativity and Quantum Cosmology · Submitted 9 Jun 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | contribution 0.98 | 0.97 | 0.16 | asserted 1.00 |
| s1 | 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. | result 0.47 | 0.79 | 0.06 | asserted 1.00 |
| s2 | We give examples of orbits showing the influence of the cosmic string. | contribution 0.69 | 0.94 | 0.05 | asserted 0.98 |
| s3 | 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. | result 0.95 | 0.93 | 0.26 | asserted 1.00 |
| s4 | 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. | result 1.00 | 0.95 | 0.30 | asserted 1.00 |
| s5 | 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. | interpretation 0.75 | 0.30 | 0.06 | asserted 0.59 |
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The paper
Original 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.
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How the literature uses it
16 arXiv papers cite this in 20 sentences
Papers citing it · 6 sentences without a confident label
Uses its method or tool 1 paper
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Eq. [ref] admits analytical solution in terms of Weierstrass $℘$-function [ref] : [equation] where the initial angle $ϕ_in$ is only dependent on $ϕ_0$ and $y_0$: [equation] Making use of [ref] we have the equation for $ω$ as [equation] which gives the solution of $ω$ in terms of $ϕ$ as [equation] Eq. [ref] is later to play a significant role in enabling null bound orbit outside the string's horizons.
Bound orbits around charged black strings · Exact Solutions of the Geodesic · 0.87
Compares with it 2 papers
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In asymptotically flat black hole space-times and even asymptotically flat space-times of black holes pierced by infinitely thin cosmic strings (see [ref] ) the perihelion shift is positive.
Detection of cosmic superstrings by geodesic test particle motion · Perihelion shift · 0.96
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However, this type of encirclement has already been observed in the space–time of a Schwarzschild black hole and Kerr black hole, respectively pierced by an infinitely thin cosmic string for sufficiently large deficit angle [ref] .
Geodesic motion in the space-time of a cosmic string · Massive particles $ε=1$ · 0.90
Cites it as background 10 papers
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The test particle motion in different space-times containing cosmic strings has been investigated in [ref] , while the complete set of orbits of test particles in the space-time of black hole pierced by an infinitely thin cosmic string has been given for a Schwarzschild black hole in [ref] and for a Kerr black hole in [ref] .
Detection of cosmic superstrings by geodesic test particle motion · Introduction · 0.94
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There have been many theoretical attempts to explain these observations [ref] .
A study of Dipolar Signal in distant Quasars with various observables · Introduction · 0.97
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Also the motion of test particles around rotating black holes [ref] and in the spacetime of a black hole which is combined by cosmic string was studied extensively [ref] .
Geodesic equations in the static and rotating dilaton black holes: Analytical solutions and applications · INTRODUCTION · 0.95
What it cites · 2 sentences without a confident label
Cites as background 1 paper
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In most cases the prediction of the detection of these objects has focused on the Cosmic Microwave background (CMB) data [ref] .
Cosmic strings and their induced non-Gaussianities in the cosmic microwave background · Conclusions · 0.99
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