Einstein Equation

  • #1
1,444
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My notes for a particular course say that [itex]G_{ab} - \Lambda g_{ab}= x T_{ab}[/itex] where [itex]x=\frac{8 \pi G}{c^4}[/itex]
Then they say that the trace of this is [itex]-R+4 \Lambda=xT[/itex]
What?
Surely that's only possible if we have [itex]+\Lambda g_{ab}[/itex] as I have seen in every other text I've ever read?

However, when we derive the Freidmann equations from this we get a [itex]( \frac{\dot{a}}{a})^2=\frac{8 \pi G}{3} \rho -\frac{k}{a^2}+\frac{\Lambda}{3}[/itex]
So if we had [itex]-\Lambda[/itex] on the LHS as suggested in the notes then this will come over to the RHS and give a + as required by the Freidmann equations but now it is all inconsistent with the trace.

This is so confusing! Can anyone clear this up? Thanks.
 

Answers and Replies

  • #2
119
0
Are you sure it isn't

[tex]G_{ab} + \Lambda g_{ab}= \frac{8 \pi G}{c^4}
T_{ab}[/tex]

in the original Equation, that is, +Λ instead of -Λ on the left-hand side?

In case your textbook/notes actually state -Λ, then there's a strong possibility of it being a typo, and in this case, just ignore it.

I'd also recommend you to notify your tutor/professor on this.
 

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