(a) The transformation from Schwarzschild coordinates (t, r, 0, 4) to outgoing Eddington- Finkelstein coordinates (u,...

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(a) The transformation from Schwarzschild coordinates (t, r, 0, 4) to outgoing Eddington- Finkelstein coordinates (u, r', 0, ') is given by U = 0 = t-r. T 0 where r. satisfies dr./dr = (1-2M/r)-¹. Use the rule for the coordinate transformation of metric components to obtain the line element in the (u, r', 0, ') coordinates. (b) Show that radial worldlines with u = const are outgoing null rays. (a) The transformation from Schwarzschild coordinates (t, r, 0, 4) to outgoing Eddington- Finkelstein coordinates (u, r', 0, ') is given by U = 0 = t-r. T 0 where r. satisfies dr./dr = (1-2M/r)-¹. Use the rule for the coordinate transformation of metric components to obtain the line element in the (u, r', 0, ') coordinates. (b) Show that radial worldlines with u = const are outgoing null rays.

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a To obtain the line element in the u r coordinates we start with the line element in Schwarzschild ... View the full answer