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...
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...
Α'2 = Σ Λ Α' (4.4) V=1...2 The instructions under the summation symbol tell us to assign the values t, x, y, z to the index v and sum the four terms that result. The value of u is left unspecified: if = 1, then this equation corresponds to the first row of equation 4.1; if u = x, it corresponds to the second line of 4.1, and so on. Equations 4.4 and 4.1 are equivalent. Equation 4.4 can be...
Step by step for #8 1) Given (1 2 3 1 0 11 1 5 2 1 A= -2 -5 -4 -1 1 ( 3 5 11 4 1 Find the basis and dimension for the row, the column spaces, and the null space NA Also, state the rank, the nullity of A 2) The subspace of W in R spanned by vectors u =(2.-2.1) v =(1,2,2) is a plane passing thru the origin. Express the vector w=(1,0.2) in the...
s={(8.60) :) :) is a basis of M3x2(R)? (d) (1 point) The set = {(1 9:(. :) : 6 1) (1 1) (1 :) :()} is linearly independent. (e) (1 point) For a linear transformation A:R" + Rd the dimension of the nullspace is larger than d. (f) (1 points) Let AC M4x4 be a diagonal matrix. A is similar to a matrix A which has eigenvalues 1,2,3 with algebraic multiplicities 1,2, 1 and geometric multiplicities 1,1, 1 respectively. 8....