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Question: this problem is quot spacetime and geometry an introduction to...

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This problem is " Spacetime and Geometry, An Introduction to General Relativity by Sean Carroll"
Chapter 3 - Problem 5

5. Consider a 2-sphere with coordinates (θ, φ) and metric (3.217) (a) Show that lines of constant longitude (φ constant) are geodesics, and that the only line of constant latitude (e constant) that is a geodesic is the equator (θ- π /2). (b) Take a vector with components νμ-(1.0) and parallel-transport it once around a circle of constant latitude. What are the components of the resulting vector, as a function of θ?

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