--- title: "Antipodal Universes in the Topology S3× R and H3× R • CBPF Index" description: "CBPF INDEX is the system that tracks the scientific and technological output of CBPF. It lists the articles, books, technical reports and other publications of the whole CBPF community." canonical_url: "https://index.cbpf.br/en/publicacoes/6ad2a767639f62b11adbb71f" locale: en meta: "og:description": "CBPF INDEX is the system that tracks the scientific and technological output of CBPF. It lists the articles, books, technical reports and other publications of the whole CBPF community." "og:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_~QW50aXBvZGFsIFVuaXZlcnNlcyBpbiB0aGUgVG9wb2xvZ3kgPG1hdGg-UzPDlyBSPC9tYXRoPiBhbmQgPG1hdGg-SDPDlyBSPC9tYXRoPg%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_~Ri4gRC4gU2Fzc2U7IEl2YW5vIERhbWnDo28gU29hcmVzOyBKYWltZSBUaW9tbm8%2Cdetalhe_1988%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmI3MWYi%2Cs_DP_wnacrkIGBEVN7.png" "og:image:height": "600" "og:image:type": image/png "og:image:width": "1200" "og:title": "Antipodal Universes in the Topology S3× R and H3× R • CBPF Index" "twitter:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_~QW50aXBvZGFsIFVuaXZlcnNlcyBpbiB0aGUgVG9wb2xvZ3kgPG1hdGg-UzPDlyBSPC9tYXRoPiBhbmQgPG1hdGg-SDPDlyBSPC9tYXRoPg%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_~Ri4gRC4gU2Fzc2U7IEl2YW5vIERhbWnDo28gU29hcmVzOyBKYWltZSBUaW9tbm8%2Cdetalhe_1988%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmI3MWYi%2Cs_DP_wnacrkIGBEVN7.png" --- > Index of every page on this site: [llms.txt](https://index.cbpf.br/llms.txt) **Physics Note****Published** # **Antipodal Universes in the Topology **S3×R\S^3\\times R\S3×R** and **H3×R\H^3\\times R\H3×R **F. D. Sasse; Ivano Damião Soares; Jaime Tiomno** 1988 [**Download PDF **0.7 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbb71f/pdf) [**Contact owner**](mailto:apub@cbpf.br?subject=Antipodal%20Universes%20in%20the%20Topology%20%3Cmath%3ES3%C3%97%20R%3C%2Fmath%3E%20and%20%3Cmath%3EH3%C3%97%20R%3C%2Fmath%3E) ## **Publication details**
Authors
F. D. Sasse; Ivano Damião Soares; Jaime Tiomno
Type
Physics Note
Status
Published
Publication date
1988
Description
On the Lie groups <math>S^3\times R \,\!</math> and <math> H^3\times R\,\!</math> a two-parameter family of left-invariant metrics <math>g_L\,\! </math> and right-invariant metrics <math>g_R \,\! </math> is introduced. The resulting space-times admit a five-parameter group of motions; in the family with topology <math> H^3\times R\,\!</math> the case occurs in which <math>g_L = g_R \,\! </math>, and this particular space-time admits a seven-parameter group of motions, with the 3-dimensional section <math>H^3\,\! </math> maximally symmetric. Global causality problems are easily characterized and it is shown how they can be avoided by the introduction of a line of singularities (strings) in the space-times. A coordinate system is defined where the left-invariant metrics <math> g_L \,\! </math> and right-invariant metrics <math>g_R \,\! </math> differ by a coordinate inversion - equivalently <math>g_L \,\! </math> and <math>g_R \,\! </math> correspond to rotating universes with opposite matter vorticity - and it is discussed how weak interaction processes could allow distinguishing the universes physically (this is the subject of a companion paper, where we introduce neutrinos as test particles in these universes). Coordinate transformations are also presented where both metrics <math>g_L \,\! </math> and <math>g_R \,\! </math> can be recast in the form of a Göde1-type metric.
Year
1988
Number
CBPF-NF-004/88
Linked to a thesis
No
Linked to a grant
No
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