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
235014-[23pp]
Grant, J.D.E.
a4590d0a-35c8-489d-aa34-c7b177d8653a
Vickers, J.A.
719cd73f-c462-417d-a341-0b042db88634
11 November 2009
Grant, J.D.E.
a4590d0a-35c8-489d-aa34-c7b177d8653a
Vickers, J.A.
719cd73f-c462-417d-a341-0b042db88634
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
Text
69575.pdf
- Accepted Manuscript
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
Catalogue record
Date deposited: 19 Nov 2009
Last modified: 14 Mar 2024 02:32
Export record
Altmetrics
Contributors
Author:
J.D.E. Grant
Author:
J.A. Vickers
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics