3. An almost-flat spacetime has metric in coordinates (zo, х, x2,T3) = (ct, x, y, z), where ηοβ = diag(-1, 1,1 , 1) is the Minkowski metric and the perturbation has is small, with hasl1. Let hue...

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3. An almost-flat spacetime has metric in coordinates (zo, х, x2,T3) = (ct, x, y, z),...

3. An almost-flat spacetime has metric in coordinates (zo, х, x2,T3) = (ct, x, y, z), where ηοβ = diag(-1, 1,1 , 1) is the Minkowski metric and the perturbation has is small, with hasl1. Let hue huv Σημι,h, where h y®ßhaß. The Einstein field equation becomes in the absence of matter and omitting terms of order ha. Consider a change of coordinates frorn zor to r/a-r" + ξα, in which the functions ξα are comparable in size to the...
4. Determine the timelike, spacelike or lightlike character of the 4-vectors: y" = (0,-1, 1,1) z" = (3,417,100) , ; in Minkowski spacetime in Cartesian coordinates 5. Show that if is a un...

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