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## Block diagonalisation of four-dimensional metrics

### Abstract

It is shown that, in 4-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 g = 0 for (, ) 2 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 equation

Topics: QA
Year: 2009
OAI identifier: oai:eprints.soton.ac.uk:69575
Provided by: e-Prints Soton

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