# Field equations Einstein-Gauss-Bonnet action

1. Dec 8, 2014

### Nick2014

Hello everyone!
I have a "great" problem with EGB action. First of all, I'm used to work with potential and scalar field, but now I have the following action
$S=\int\sqrt{-g}\left(2\beta +R+\alpha GB\right)d^6 x$

where GB is the six-dimensional Gauss-Bonnet term, R is the scalar curvature and $2\beta$ is a cosmological constant. $\alpha$ is a coupling parameter. Well, I want to write Einstein equations, but I don't know how to calculate stress-energy tensor $T$... Thanks in advance

2. Dec 8, 2014

### Chalnoth

See the derivation of the four-dimensional einstein field equations:

Basically, you add the matter action to the gravitational action above.

3. Dec 8, 2014

### Nick2014

Thanks :) but in my case we are in six dim not four... Then, there is no matter terms... My professor says this...

4. Dec 8, 2014

### Chalnoth

If you're not going to have any matter terms, then you're not going to have a stress-energy tensor. The analog to the Einstein field equations without any matter action would have some terms related to spatial curvature set equal to zero.

5. Dec 8, 2014

### Nick2014

very thanks :)