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I entered my coordinates like this:

M = Manifold(3, 'M', structure='Lorentzian')X.<t,p,ph> = M.chart(r't p ph:\phi')X

Then defined my metric-tensor like this:

g = M.metric()g[0,0], g[1,1] = -1, 1 g[2,2] = (5*p^2+4*t^2)g.display()

How to transform the metric under the coordinate change of r=sqrt(5p^2+4t^2)? And once I do that, can the Christoffel symbols be calculated from the new metric instead of the old one, and in terms of t and r?

I entered my coordinates like this:

M = Manifold(3, 'M', structure='Lorentzian')X.<t,p,ph> structure='Lorentzian')
X.<t,p,ph> = M.chart(r't p ph:\phi')X
ph:\phi')
X

Then defined my metric-tensor like this:

g = M.metric()g[0,0], M.metric()
g[0,0], g[1,1] = -1, 1  g[2,2] = (5*p^2+4*t^2)g.display()
(5*p^2+4*t^2)
g.display()

How to transform the metric under the coordinate change of r=sqrt(5p^2+4t^2)? r=sqrt(5*p^2+4*t^2)? And once I do that, can the Christoffel symbols be calculated from the new metric instead of the old one, and in terms of t and r?