J D E Grant and J A Vickers 2009 Class. Quantum Grav. 26 235014 doi:10.1088/0264-9381/26/23/235014
Block diagonalization of four-dimensional metrics
J D E Grant1 and J A Vickers2
Show affiliationsIt is shown that, in four dimensions, it is possible to introduce coordinates so that an analytic metric locally takes block diagonal form, i.e. one can find coordinates such that gαβ = 0 for (α, β) 
S where S = {(1, 3), (1, 4), (2, 3), (2, 4)}. We call a coordinate system in which the metric takes this form a 'doubly biorthogonal coordinate system'. We show that all such coordinate systems are determined by a pair of coupled second-order partial differential equations.
- PACS
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04.20.Fy Canonical formalism, Lagrangians, and variational principles
- MSC
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35L10 General theory of second-order, hyperbolic equations
83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
- Subjects
- Dates
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Issue 23 (7 December 2009)
Received 2 February 2009, in final form 6 October 2009
Published 11 November 2009
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Block diagonalization of four-dimensional metrics
J D E Grant and J A Vickers 2009 Class. Quantum Grav. 26 235014
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