Analytical solutions of bound timelike geodesic orbits in Kerr spacetime
193 citations recorded by the source corpus.
We derive the analytical solutions of the bound timelike geodesic orbits in Kerr spacetime. The analytical solutions are expressed in terms of the elliptic integrals using Mino time λ as the independent variable. Mino time decouples the radial and the polar motion of a particle and hence leads to forms more useful to estimate three fundamental frequencies, radial, polar and azimuthal motion, for the bound timelike geodesics in Kerr spacetime. This paper gives the first derivation of the analytical expressions of the fundamental frequencies. This paper also gives the first derivation of the analytical expressions of all coordinates for the bound timelike geodesics using Mino time. These analytical expressions should be useful not only to investigate physical properties of Kerr geodesics but more importantly to applications related to the estimation of gravitational waves from the extreme mass ratio inspirals.
Subfields: Astronomy and Astrophysics
View Paper: https://www.semanticscholar.org/paper/ab3b705099f0eb1f3e6725c800f4b8ae7183c0be
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Astronomy and Astrophysics
Citations in the corpus
- Black hole perturbation theory and gravitational self-force (2021, methodology): “The solution to the geodesic equation can also be put in closed, analytical form [65] by expressing ψα(λ ) in terms of elliptic integrals and their inverses (the Jacobi elliptic functions).”