Dear Colleagues,
I'm a new addition to this list. So far I'm not familiar with Maxima, but
wish to explore if it can be used efficiently to do certain computations
in General Relativity. My hope is to reach experts in CSA (which I'm not
at all) who might be able to give me valuable guiding suggestions on how I
should try to use, Maxima or any other CSA, for such computations.
I'll now explain the computation. The context is an arbitrary submanifold
embedded in a higher dimensional manifold. One wishes to compute tubular
expansion (covariant Taylor expansion) of tensors around the submanifold.
Exact results for vielbein components have been derived in
http://arxiv.org/abs/arXiv:1203.1151
Expansion of the metric components have also been computed explicitly up
to 10th order. Please see the expressions up to 2nd order in equations
(2.3) of
http://arxiv.org/abs/arXiv:1202.2735
Here $(x, y)$ are a local Fermi normal system such that $\{x^{\alpha} \}$
is a general coordinate system on the submanifold and $\{ y^A \}$ are
transverse coordinates. Therefore, lower case Greek indices run over the
dimension of the submanifold and upper case Roman indices run over the
dimension of the transverse space. The barred quantities in the above
equations, which appear as expansion coefficients, are certain tensors of
the total space evaluated on the submanifold.
Given this, the goal is to compute Christoffel symbols, curvature etc to a
desired order.
So my questions are: Should it be possible to develop these computations
easily and efficiently using Maxima? If yes, may I get some help? If no,
will it be possible to use an alternative CSA, preferably free, to do
this?
Thanks very much in advance.
Regards
Partha