# Problem with Metric Tensor coordinate change.

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.

edit retag close merge delete

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...

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

Sort by » oldest newest most voted

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): ...})


by

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.

more

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
])


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