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SPACE–TIME STRUCTURE AND SPINOR GEOMETRY

Part of: General relativity

Published online by Cambridge University Press:  01 October 2008

GEORGE SZEKERES  and
LINDSAY PETERS
GEORGE SZEKERES
Affiliation:
School of Mathematics, University of New South Wales, Sydney 2052, Australia (deceased)
LINDSAY PETERS*
Affiliation:
Pacific Knowledge Systems, Australian Technology Park, Sydney 1430, Australia (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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The structure of space–time is examined by extending the standard Lorentz connection group to its complex covering group, operating on a 16-dimensional “spinor” frame. A Hamiltonian variation principle is used to derive the field equations for the spinor connection. The result is a complete set of field equations which allow the sources of the gravitational and electromagnetic fields, and the intrinsic spin of a particle, to appear as a manifestation of the space–time structure. A cosmological solution and a simple particle solution are examined. Further extensions to the connection group are proposed.

Keywords

space–time structurespinor geometrygravitational fieldelectromagnetic field

MSC classification

Secondary: 83C05: Einstein's equations (general structure, canonical formalism, Cauchy problems)
Type
Research Article
Information
The ANZIAM Journal , Volume 50 , Issue 2 , October 2008 , pp. 143 - 176
Copyright
Copyright © Australian Mathematical Society 2009

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