# Einstein hilbert action

1. Apr 27, 2007

### Terilien

Can someone explain to me why this is the appropriate action?It makes some sens that that would be used, but I'd like a detailed explanation from someone familiar with the topic.

Why is it the one that yields the proper equations?

Last edited: Apr 27, 2007
2. Apr 27, 2007

### masudr

Well, for a start, you can derive the field equations by setting variations of this action with respect to the metric equal to zero. This is done in many GR texts.

3. Apr 27, 2007

### Terilien

Yes but what is the intuition behind it? What lead hilbert to choose that particular action?

4. Apr 27, 2007

### masudr

Can you think of a simpler scalar that encodes the curvature of spacetime? The Ricci scalar is a fairly obvious choice.

5. Apr 27, 2007

### Terilien

So essentially it used because its the simplest, most general(encodes curvature) involves the inverse metric, the ricci tensor, etc.. and such. So essentially its simple and encodes all the information that we may want tin the field equations...

This is the first time I've emcountered this topic(variational mechanics) so it seems quite exotic. Its very interesting though.

It would however be nice, to gain whatever insight I can into this principle and this topic in general.

Last edited: Apr 27, 2007