Physics NotePublished
Geodesics in Gödel-Type Space-Times
M. O. Calvao; Ivano Damião Soares; J. Tiomno
1988
Publication details
- Authors
- M. O. Calvao; Ivano Damião Soares; J. Tiomno
- Type
- Physics Note
- Status
- Published
- Publication date
- 1988
- Description
- We investigate the geodesic curves of the homogeneous Godel-type space-times, which constitute a two-parameter <math>(\ell\!</math> and <math> \Omega)\,\!</math> class of solutions presented to several theories of gravitation (general relativity, Einstein?Cartan and higher derivative). To this end, we first examine the qualitative properties of those curves by means of the introduction of an effective potential and then accomplish the analytical integration of the equations of motion. We show that some of the qualitative features of the free motion in Gödel's universe <math>(\ell^2=2\Omega^2)\,\!</math> are preserved in all space-times, namely:(a) the projections of the geodesics onto the 2-surface <math>(r,\varphi)\,\!</math> are simple closed curves, and (b) the geodesics for which the ratio of azymuthal angular momentum to total energy,<math>\gamma\,\!</math>, is equal to zero always cross the origin <math>r = \emptyset\,\!</math>. However, two new cases appear: (i) radially unbounded geodesics with <math>\gamma\,\!</math> assuming any (real) value, which may occur only for the causal space-times <math>(\ell^2 \ge 4\Omega^2\,\!)</math>, and (ii) geodesics with <math> \gamma \,\!</math> bounded both below and above,which always occur for the circular family <math>(\ell^2 < \emptyset\,\!)</math> of space-times.
- Year
- 1988
- Number
- CBPF-NF-065/88
- Linked to a thesis
- No
- Linked to a grant
- No