Immersions of Einstein-Riemann spacetimes in five-dimensional flat spaces

Details Immersions of Einstein-Riemann spacetimes in five-dimensional flat spaces Immersions of Einstein-Riemann spacetimes in five-dimensional flat spaces

Nov 2000

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000cqgra..17.4715e&link_type=abstract

Classical and Quantum Gravity, Volume 17, Issue 22, pp. 4715-4732 (2000).

Computer Science

4

Scientific paper

Gauge-theoretic constructs and Cartan's method of moving coframe fields are used to obtain immersions of four-dimensional Einstein-Riemann spacetimes in flat five-dimensional spaces. A generalization of Cayley's representation theorem (for matrix elements of SO(n)) to the groups SO(2,3) and SO(1,4) leads to a choice of the four immersion parameters such that all salient geometric quantities are evaluated in terms of rational algebraic functions. After an analysis of the general immersion problem, considerations are restricted to classes of immersions for which the matrix of gauge curvature 2-forms is of maximal rank. All solutions of these immersion problems are shown to be generated by vector spaces of 1-form fields, so that there is a superposition principle at this level. These 1-form fields lead to families of associated metric and curvature tensor fields with specific composition laws. Several multiple-parameter families of immersions are calculated explicitly. A spherically symmetric, deflation-inflation model with a central black hole is presented.

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