| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] SN Bose Natl Ctr Basic Sci, JD Block, Sect 3, Kolkata 700098 - India
[2] Univ Sao Paulo, Inst Fis, C Postal 66318, BR-05314970 Sao Paulo, SP - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS; v. 13, n. 4 APR 2016. |
| Web of Science Citations: | 3 |
| Abstract | |
Bianchi-IX four metrics are SU(2) invariant solutions of vacuum Einstein equation, for which the connection-wise self-dual case describes the Euler top, while the curvaturewise self-dual case yields the Ricci flat classical Darboux-Halphen system. It is possible to see such a solution exhibiting Ricci flow. The classical Darboux-Halphen system is a special case of the generalized one that arises from a reduction of the self-dual Yang-Mills equation and the solutions to the related homogeneous quadratic differential equations provide the desired metric. A few integrable and near-integrable dynamical systems related to the Darboux-Halphen system and occurring in the study of Bianchi-IX gravitational instanton have been listed as well. We explore in details whether self-duality implies integrability. (AU) | |
| FAPESP's process: | 13/17765-0 - Non-commutative Geometry and Emergent Gravity |
| Grantee: | Raju Roychowdhury |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |