# Field equations Einstein-Gauss-Bonnet action

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

## Answers and Replies

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

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

Nick2014
Thanks :) but in my case we are in six dim not four... Then, there is no matter terms... My professor says this...