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Introductory Physics Homework Help
GR: Quick Q, conservation energy, stuck on algebra
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[QUOTE="binbagsss, post: 4959746, member: 252335"] I'm stuck on deriving the follow. Context: FRW Metric, dust dominated universe, use of conservation of energy-momentum tensor. I'll now state all the equations I can see are relevant. (But just in case the source is [url]http://arxiv.org/pdf/gr-qc/9712019.pdf[/url] and it's eq 8.43). ## \frac{d}{dt}(\rho a^{3}) = a^{3}(\dot{\rho}+3\rho\frac{\dot{a}}{a}) = -3pa^{2}\dot{a} ##, and it's the last equation I am stuck on. I am getting it to be ## -3 \rho a^{2}\dot{a} ##... 2. Homework Equations : ## 0 = \bigtriangledown_{a}T^{a}_{0}=-\partial_{0}\rho=3\frac{\dot{a}}{a}(\rho +p) ## [1] and using ##p=w\rho ## this becomes: ##\frac{dot{\rho}}{\rho}=-3(1+w)\frac{\dot{a}}{a}##, [2] where for dust w takes the value 0. 3. The Attempt at a Solution So I believe the last equality comes from [1], and for dust we have P=0, which is why I get ## -3 \rho a^{2}\dot{a} ##. (the second equality I can see is just differetiating). Thanks in advance. [/QUOTE]
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Introductory Physics Homework Help
GR: Quick Q, conservation energy, stuck on algebra
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