Tensors and Relativity: Hints 6

• (2) This is straight out of section 6.5.1 of the lecture notes.

• (3) First write down the standard transformation laws which take you from (x,y,z) to . Next calculate the basis vectors and then the metric from . The metric for a 2- sphere, then follows by taking r=1, so dr=0.

• (4) Here it is enough to show that the Christoffel symbols all vanish.

• (5) The only non- zero component is , so that's all you need to calculate.

• (6) In both parts use a local inertial frame to prove the results.

• (7) Calculate , where is an affine parameter along the geodesic.

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