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S Mar 6, 2022 at 6:54 history edited Níckolas Alves CC BY-SA 4.0
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S Mar 6, 2022 at 6:54 history suggested user320397 CC BY-SA 4.0
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Aug 11, 2017 at 14:05 comment added Cham The Einstein equation is really a second order equation, with some constraints from the Bianchi identity. Thus equation (1) is a constraint on equation (2) (second order equation). Equation (3) is a consequence of the Bianchi identity which implies local conservation of energy-momentum : $\nabla_{\mu} \, T^{\mu \nu} = 0$. This one gives (3).
Aug 11, 2017 at 13:56 comment added Cham Your equations (1) and (2) are missing some terms. They should be these (with the cosmological constant) : \begin{equation}\tag{1} \frac{\dot{a}^2}{a^2} + \frac{k}{a^2} = \frac{8 \pi G}{3} \, \rho + \frac{\Lambda}{3}, \end{equation} and \begin{equation}\tag{2} \frac{\ddot{a}}{a} = -\: \frac{4 \pi G}{3} ( \rho + 3 p) + \frac{\Lambda}{3}. \end{equation} euqation (1) is a first order differential equation, while (2) is second order. This is why most authors say that (1) is the first equation of FL, while (2) is the second equation of FL.
Nov 12, 2011 at 1:24 vote accept Joss L
Aug 5, 2011 at 9:39 history tweeted twitter.com/#!/StackPhysics/status/99414115054915584
Aug 4, 2011 at 19:11 answer added Benjamin Horowitz timeline score: 5
Aug 4, 2011 at 17:27 history asked Joss L CC BY-SA 3.0