Now we compute . First, the Riemann tensor has the following definition:

so

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# #2 – Hilbert – Einstein action – Part 2

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# #2 – Hilbert – Einstein action – Part 1

# #1 – Proof: variation of a determinant

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Now we compute . First, the Riemann tensor has the following definition:

so

Continue reading “#2 – Hilbert – Einstein action – Part 2”

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The Hilbert-Einstein action is:

Einstein equations (the evolution equations of the metrig ) can be found if we set .

By definition:

so

Thus:

If is a metric tensor, so we have:

Equating terms proportional to :

Finally: