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Block diagonalisation of four-dimensional metrics

Block diagonalisation of four-dimensional metrics
Block diagonalisation of four-dimensional metrics
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 equations
differential geometry, general relativity
0264-9381
235014-[23pp]
Grant, J.D.E.
a4590d0a-35c8-489d-aa34-c7b177d8653a
Vickers, J.A.
719cd73f-c462-417d-a341-0b042db88634
Grant, J.D.E.
a4590d0a-35c8-489d-aa34-c7b177d8653a
Vickers, J.A.
719cd73f-c462-417d-a341-0b042db88634

Grant, J.D.E. and Vickers, J.A. (2009) Block diagonalisation of four-dimensional metrics. Classical and Quantum Gravity, 26, 235014-[23pp]. (doi:10.1088/0264-9381/26/23/235014).

Record type: Article

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 equations

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More information

Submitted date: 2 February 2009
Published date: 11 November 2009
Keywords: differential geometry, general relativity
Organisations: Applied Mathematics

Identifiers

Local EPrints ID: 69575
URI: http://eprints.soton.ac.uk/id/eprint/69575
ISSN: 0264-9381
PURE UUID: d5d62d95-18af-4232-bb1d-c6192481c916
ORCID for J.A. Vickers: ORCID iD orcid.org/0000-0002-1531-6273

Catalogue record

Date deposited: 19 Nov 2009
Last modified: 09 Jan 2022 02:33

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Contributors

Author: J.D.E. Grant
Author: J.A. Vickers ORCID iD

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