Consider the line element ds² = −dt² + dx². Determine the line element after the coordinate transformation t = X sinh T, x= X cosh T. Write down the metric in the new coordinates. Determine the Riemann curvature tensor for this metric, without performing a detailed calculation.
Consider the line element ds² = −dt² + dx². Determine the line element after the coordinate transformation t = X sinh T, x= X cosh T. Write down the metric in the new coordinates. Determine the Riemann curvature tensor for this metric, without performing a detailed calculation.
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[General Theory of Relativity]
Transcribed Image Text:Consider the line element
ds²-dt² + dx².
=
Determine the line element after the coordinate transformation
t = X sinh T, x = X cosh T.
Write down the metric in the new coordinates. Determine the Riemann curvature tensor for this
metric, without performing a detailed calculation.
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