Show that in the coordinate system {x^0̂, x^1̂, x^2̂, x^3̂} of Eqs. (26.25b), the coordinate basis vectors at x^ĵ = 0 are Eqs. (26.24), and, accurate through first order in distance from x^ĵ = 0, the spacetime line element is Eq. (26.26); that is, errors are no larger than second order.

Equations.

Transcribed Image Text:

=e*8 e=e= |==e- Ər 3 ē = 1 a rae ēô = 1 r sin 2 ap eet, e²=e^r, ervo, e = r sin 06. = (26.24a) (26.24b)