The Lorentz Group in General Relativity

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princeton118
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What role does the Lorentz Group play in the General Relativity ?
 
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Local or infinitesimal geometry is Euclidean, special relativity hols and Lorentz transfomation law is used. The finite geometry is non-Euclidean, special relativity does not hold and the tranfomation law are genrall covariant tranformations.