Philosophaie
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Schwarzschild solution for Planetary Motion:
##g_{ij}= \left( \begin{array}{cccc}
\frac{1}{(1-(\frac{2*m}{r}))} & 0 & 0 & 0 \\
0 & r^2 & 0 & 0 \\
0 & 0 & r^2*(sin\theta)^2 & 0 \\
0 & 0 & 0 & c^2*(1-\frac{2*m}{r})
\end{array} \right)
##
where ##m=\frac{G*(Mass of Sun)}{c^2}##
My question is how do you find the Resultant Contravarient Position Vector.
##x^{'i} = \left( \begin{array}{c} r' \\ \theta' \\ \phi' \\ t' \end{array} \right)##
given the Contravarient Position Vector.
##x^{i} = \left( \begin{array}{c} r \\ \theta \\ \phi \\ t \end{array} \right)##
from the Schwarzschild Metric Tensor.
##g_{ij}= \left( \begin{array}{cccc}
\frac{1}{(1-(\frac{2*m}{r}))} & 0 & 0 & 0 \\
0 & r^2 & 0 & 0 \\
0 & 0 & r^2*(sin\theta)^2 & 0 \\
0 & 0 & 0 & c^2*(1-\frac{2*m}{r})
\end{array} \right)
##
where ##m=\frac{G*(Mass of Sun)}{c^2}##
My question is how do you find the Resultant Contravarient Position Vector.
##x^{'i} = \left( \begin{array}{c} r' \\ \theta' \\ \phi' \\ t' \end{array} \right)##
given the Contravarient Position Vector.
##x^{i} = \left( \begin{array}{c} r \\ \theta \\ \phi \\ t \end{array} \right)##
from the Schwarzschild Metric Tensor.