## Physics & Astronomy ETDs

## Publication Date

7-2-1974

## Abstract

The timelike and null geodesics in the Kerr metric describe important properties of the space surrounding a rotating black hole. The general characteristics of these geodesics, with an emphasis on those on the axis of symmetry and the equatorial plane, are found in this paper. On the axis of symmetry, the behavior of all timelike and null geodesics is completely described. The accessibility of various spaces added for geodesic completeness in the extended manifold is found by making local observations of geodesics in one coordinate patch from geodesics in another. The analysis on the equatorial plane shows that for a given range [refer to the manuscript] angular momentum, P_{t}, if the energy, -P_{t}, is in the [refer to the manuscript] ,the geodesic, for r > r_ , is in the I region and, for r < r_, is in the III' region in Carter's version of the extended manifold. The energy and momentum of circular orbits, as functions of r and a, in the equatorial plane are found. The limits of the motion in thee direction are found explicitly as functions of the constants of the motion. This analysis shows that there is geodesic motion on the equatorial plane that is unstable in the 6 direction. This instability is most pronounced for all zero angular momentum unbound orbits; in this case, there is no minimum or maximum 6, and any perturbation could carry the geodesic to the axis of symmetry. Lastly, to show the nature of a surface containing 6 geodesics, Carter's null surface is imbedded in a three dimensional Minkowski space.

## Degree Name

Physics

## Level of Degree

Doctoral

## Department Name

Physics & Astronomy

## First Committee Member (Chair)

J. Daniel Finley

## Second Committee Member

David S. King

## Third Committee Member

Byron Dale Dieterle

## Language

English

## Document Type

Dissertation

## Recommended Citation

St. John, Richard H.. "General Geodesic Motion in the Extended Kerr Manifold." (1974). https://digitalrepository.unm.edu/phyc_etds/223