Problem with Metric Tensor coordinate change.

asked 2021-07-04 22:32:34 +0200

I define a M manifold with three charts, I then define a metric on one of the charts MH. I then want to see the metric components in one of the other charts BL. I have defined differential maps between the charts.

gMann(MH) works and I can display the components but,

gMann(BL) gives the error:

ValueError: the provided domain is not a subset of the field's domain

print(subdomain,self._restrictions) gives 'Open subset MBL of the 4-dimensional Lorentzian manifold M {}' .

How do I make this work please? I will post the code in comments below.

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Link to code at my website. The problem surfaces in cell 6. The function definitions between cell two and six can be ignored.

http://alan.atstafford.co.uk/BlackHol...

AlanTStafford ( 2021-07-04 22:38:50 +0200 )edit

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answered 2021-07-05 17:07:44 +0200

eric_g
8209 ●10 ●61 ●162 https://luth.obspm.fr/...

You should define the transition maps via the method transition map of charts and not as a differentiable map, i.e. replace

to_MH_from_BL = M.diff_map(MMH, {(BL, MH): ...})

to_MH_from_BL = BL.transition_map(MH, ...)

and then use

show(gMann.display(BL.restrict(MMH.intersection(MBL))))

instead of show(gMann.display(BL) since gMann is not defined on BL's domain, as said in the error message.

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Thank you, answer accepted. I was nearly there trying restrict but hadn't got to using an intersection. I have the maps the wrong way round in the code. The ones I am using are.

to_MH_from_BL = BL.transition_map(MH,  [       t, 
                                               r, 
                                               cos(th), 
                                               phi
                                           ])

to_BL_from_MH = MH.transition_map(BL,      [   t,
                                               x,
                                               arccos(y),
                                               phi
                                           ])

AlanTStafford ( 2021-07-05 17:41:35 +0200 )edit

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