(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm given the metric for Einstein's universe,

ds^{2}= c^{2}dt^{2}- dr^{2}/(1 - kr^{2}) - r^{2}d(theta)^{2}- r^{2}sin^{2}(theta)d(phi)^{2}

and asked to find the null geodesic equations and show that in the plane theta=[tex]\pi[/tex]/2, the curves satisfy the equation:

(dr/d(phi))^{2}= r^{2}(1-kr^{2})(mr^{2}-1)

where m is a constant

2. Relevant equations

3. The attempt at a solution

I know I have to use "The Integral" (I'm not sure if thats a widely accepted name for it or if not what the real name of it is), and that for finding null geodesic equations I have to set it equal to zero, which gives

0 = g_{ij}[tex]\stackrel{.}{x}[/tex]^{i}[tex]\stackrel{.}{x}[/tex]^{j}

where [tex]\stackrel{.}{x}[/tex] = dx/d(mu), or essentially dx/ds, but I'm confused about how to do this, every time I take my work in to be looked at, my professor says I'm doing something else and that my work is irrelevant to the question, so I'm stumped. He's told me that I'll also need to use Christoffel symbols to get to the dr/d(phi) form in the second part of the equation, but without the first part of the problem solved I can't do that, so far as I can tell. Can anyone tell me what I'm missing here?

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# Homework Help: Obtaining null geodesic eq.'s

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