Physics NotePublished
Antipodal Universes in the Topology and
F. D. Sasse; Ivano Damião Soares; J. Tiomno
1993
Publication details
- Authors
- F. D. Sasse; Ivano Damião Soares; J. Tiomno
- Type
- Physics Note
- Status
- Published
- Publication date
- 1993
- Description
- We construct spacetimes with the topology of the Lie groups <math>H^3\times R\,\!</math> and <math>S^3\times R\,\!</math> by introducing left-invariant metrics <math>g_L\,\!</math> and right-invariant metrics <math>g_R\,\!</math> on the group manifold. <math>g_L\,\!</math> and <math>g_R\,\!</math> are related isometrically to each other by the Lie group inverse map, which induces an anti-isomorphism between the Lie algebra of the left-invariant vector fields and that of right-invariant vector fields. We introduce a coordinate system where the inverse map group operation is expressed by a coordinate inversion. We denote these universes antipodal. The resulting spacetimes admit by construction a <math>G_5\,\!</math> group of motions. In the family with topology <math>H^3\times R\,\!</math> there occurs the particular case <math>g_L=g_R\,\!</math>, which admits a <math>G_7\,\!</math> group of motions with the 3-dim sections <math>H^3\,\!</math> maximally symmetric. The existence of acausal curves in these spacetimes is examined. Some of them are avoided by modifying the connectivity-in-the-large of the manifold, while others can be avoided by the introduction of a line of singularities in the spacetime manifold. We show that <math>g_L\,\!</math> and <math>g_R\,\!</math> correspond to rotating universes with matter vorticity of opposite sign. Massless neutrinos (produced via weak interaction processes) can be used as a probe to distinguish physically the antipodal universes, because the ''active'' transformation leading <math>g_L\,\!</math> into <math>g_R\,\!</math> also transforms neutrinos in antineutrinos (or vice versa).
- Year
- 1993
- Number
- CBPF-NF-072/93
- Linked to a thesis
- No
- Linked to a grant
- No