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

 

[Chalnoth]

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:
http://www.science20.com/standup_ph...d_equation_derivation_about_dozen_steps-90263

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...

 

[Chalnoth]

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

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.

 

[Nick2014]

very thanks :)