stress energy tensor

[alejandrito20]

In a space time [math]5D[/math], the action for the brane [math]4D[/math] is:

 

[math] \int dx^4 \sqrt{-h}[/math]

 

In the Randall Sundrum the action for the hidden brane is:

[math] V_0\int dx^4 \sqrt{-h}[/math], where [math]V_0[/math] is the tension on the brane hidden.

 

follow the stress energy tensor

 

[math] T_{MN}= V_0 h_{uv} \delta^u_M \delta^v_N \delta(\phi)[/math], where [math]\phi[/math] is the extra dimention.

 

In other paper, where [math]T_{MN}[/math], for example in the friedman equation in http://arxiv.org/abs/hep-th/0303095v1 (page 6)...

 

[math] T_{00}= -\rho \delta(\phi)[/math]

[math] T_{ii}= p \delta(\phi)[/math]

the other component are zero.

 

I understand thar [math]\rho , p[/math] are energy density and presion

 

If , i use other embedding my energy stress tensor is

[math] T_{00}= - \delta(\phi)[/math]

[math] T_{ii}= \delta(\phi)[/math]

[math] T_{0 \phi}= \delta(\phi)[/math]

[math] T_{\phi \phi}= \delta(\phi)[/math]

 

¿can i to multiply the each component of the stress tensor by differents constants???...for example:

[math] T_{00}= - k_1 \delta(\phi)[/math]

[math] T_{ii}= k_2 \delta(\phi)[/math]

[math] T_{0 \phi}= k_3 \delta(\phi)[/math]

[math] T_{\phi \phi}= k_4 \delta(\phi)[/math]

Edited May 23, 2011 by alejandrito20