S Bonanos 1996 Class. Quantum Grav. 13 2473 doi:10.1088/0264-9381/13/9/012
S Bonanos
Show affiliationsThe `post-Bianchi equations', i.e., the extra integrability conditions that arise when a choice of frame is made, provide additional constraints on the mathematical problem of integrating the vacuum Einstein equations. It is shown that these equations give an expression for the divergence of the connection in terms of the Newman - Penrose variables. Explicit expressions for the spin-coefficients, satisfying the Bianchi identities, are also given. A matrix integrability theorem is formulated and used to transform the Einstein equations into a new matrix form.
04.20.Gz Spacetime topology, causal structure, spinor structure
83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
Issue 9 (September 1996)
Received 9 October 1995, in final form 20 May 1996
S Bonanos 1996 Class. Quantum Grav. 13 2473
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