In the case of T3-topology, there are coordinates such that the metric takes the form
Here
The values of the constants and
in Equation (1
) are of no importance in practice. Consequently,
can be taken to equal 1 and
can be taken to equal 0. In order to arrive at the form of the metric we
shall actually be using, let us set
and
. Furthermore, we define
,
,
,
, where we have used the fact that
are the components of a
positive definite matrix. Since
is also a symmetric matrix with unit determinant, we obtain
In the case of S3 and S2 × S1 topology, the metric can be written
where
http://www.livingreviews.org/lrr-2010-2 |
Living Rev. Relativity 13, (2010), 2
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