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lostphysicist
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Homework Statement
Write down an orthonormal basis of 1 forms for the rotating C-metric
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Use the result to find the corresponding dual basis of vectorsSee attached file for metric and appropriate equations
The two equations on the left are for our vectors. the equations on the right are for our 1-forms/dual-vectors.
The Attempt at a Solution
g^μν= inverse metric on the manifold
η^μν=inverse minkowski metric=diag(-1,1,1,1)= minkowski m etric
E_a=non coordinate basis vectors for metric
Θ_a=non coordinate 1-forms for metric
I'm confused how we read off the g_μν from the metric above. Will this be equal to g^μν?
Do we have to expand the brackets or are the coordinates
1. dt-αx^2dφ
2.dy
3.dx
4.dφ+αx^2
and the g_μν components just the factors in front of these square rooted? What are the vierbeins?
Any help would be appreciated.
Thanks