xAct - Signature of the metric in general dimensions - ConstantSymbols and integers

[Alejandro Jiménez]

Hi!

I am working with a general dimension:

DefConstantSymbol[dimM]

DefManifold[M, dimM, {a, b, c, d, e, f, g, h, i, j, k, l, m, n}]

Suppose I want to choose the signature (+ -...-) for the metric. What I did was:

DefMetric[{1, dimM-1, 0},  metricg[-a, -b], ...(bla bla)...]  

but I get an error if I do not tell Mathematica that dimM is (or behaves as) an integer greater than 1.

I am not an expert in Mathematica, so I do not know if there is a way using its standard options; I mean, without using a ConstantSymbol as I did and, instead, a couple of auxiliary variables MetricPlusIndex and MetricMinusIndex (not declared as ConstantSymbols, just default Mathematica objects) and indicating that they are going to be integers the whole time.

Is it possible? Thanks in advance!

Best regards,

Alejandro JC

-------------

Note: 

with the other convention (- +...+), since you only have one minus, you could avoid the problem defining 

DefMetric[-1,  metricg[-a, -b], ...(bla bla)...] 

and it is independent of the dimension.

[Thomas Bäckdahl]

Hi!

The first argument of DefMetric can either be the signature, i.e. a list with 3 numbers or just the corresponding determinant.
Unfortunately, this was not designed for symbolic dimensions so the checks are a bit too restrictive.
Perhaps these checks should be rewritten, but instead of doing that, you could try to bypass the tests in this way

Abs[signDetM] ^= 1
DefMetric[signDetM, met[-a, -b], CD]
signDetM = (-1)^(dimM - 1)
SignatureOfMetric[met] ^= {1, dimM - 1, 0}

I hope this works, but I can not guarantee that some function somewhere will complain due to a symbolic SignDetOfMetric. Most  xAct functions will only use SignDetOfMetric, not SignatureOfMetric, so that is the most important part to get right.

Reagrds
Thomas

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[Alejandro Jiménez]

Thanks for your reply! It works. If I find any problematic consequence, I will write it here.

Alejandro JC