Physics · Paper · June 2022
Particle Geodesics in the Kerr Spacetime
The Kerr spacetime is investigated. The singularity structure and horizon structure of the spacetime are explored. Two sets of equations of motion for a particle orbiting a Kerr black hole are derived: the first by the calculating nonzero Christoffel symbols of the metric and utilizing the geodesic equation; the second by dot products of Killing vectors and the four-velocity. The effective potential of the radial motion is found and analyzed in comparison with the Schwarzschild effective potential. The Kerr/CFT correspondence and its recent use in predicting polarimetric images of the supermassive black hole in the galaxy M87 is also discussed briefly. An overview of special relativity, general relativity, and orbits is provided in the appendix to serve as background information for the body of the paper. The Mathematica programs used for this paper can be found here: https://bit.ly/3dlwYH7.