Tensor Analysis Problems And Solutions Pdf Free [patched] File

Get comfortable using the metric tensor to raise and lower indices.

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(excerpt from a free PDF): (a) ( g_rr=1, g_\theta\theta=r^2, g^rr=1, g^\theta\theta=1/r^2 ), others 0. (b) ( \Gamma^r_\theta\theta = -r ), ( \Gamma^\theta_r\theta = \Gamma^\theta_\theta r = 1/r ). (c) ( \nabla_\theta V^\theta = \partial_\theta V^\theta + \Gamma^\theta_\theta r V^r = \cos\theta + (1/r)\cdot r^2 = \cos\theta + r ).