On the second integrals of geodesics in the Kerr field

Details On the second integrals of geodesics in the Kerr field On the second integrals of geodesics in the Kerr field

Mar 1976

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976ap%26ss..40...39k&link_type=abstract

Astrophysics and Space Science, vol. 40, Mar. 1976, p. 39-61.

Physics

9

Field Theory (Physics), Geodesic Lines, Relativity, Space-Time Functions, Gravitational Waves, Trajectory Analysis

Scientific paper

Second integrals of the geodesic equations for the Kerr metric in Boyer-Lindquist coordinates are analyzed qualitatively by investigating a dynamic system of first integrals. The structure of phase-space decomposition into phase trajectories is studied along with test-particle motion in the neighborhood of singular points and the location of bifurcation points in parameter space. Separate analyses are performed for the equation of latitude and the radial equation. General analytical properties of the second integrals of geodesics for the Kerr solutions are discussed, and six theorems concerning these integrals are proven.

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