prob3

# prob3 - d s 2 = e A ( r ) b d r 2 + r 2 d θ 2 + r 2 sin 2...

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A.V. Manohar Ph225A: General Relativity Problem Set 3 1. Show that - g d 4 x is invariant under a change of coordinates, where g = det g μν and d 4 x = d x 0 d x 1 d x 2 d x 3 . 2. Let x μ ( s ) be a curve. Show that d x μ / d s transforms as a tensor. Find the transforma- tion law for d 2 x μ / d s 2 , and show that it does not transform as a tensor. 3. Find the transformation law for Γ λ μν under a change of coordinates. (Both the forms given in lecture). 4. Consider the static spherically symmetric metric
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Unformatted text preview: d s 2 = e A ( r ) b d r 2 + r 2 d θ 2 + r 2 sin 2 θ d φ 2 B-e B ( r ) d t 2 Find the Christo±el symbols Γ λ μν . 5. Show that g αβ (d x α / d s )(d x β / d s ) is constant along a curve which is a solution of the geodesic equation. 6. Find the equations which extremize i d s g αβ d x α d s d x β d s 1...
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## This note was uploaded on 04/19/2008 for the course PHYS 225 taught by Professor Manohar during the Fall '07 term at UCSD.

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