Stress Energy Tensor in 5D Space-Time: Action for Brane and Hidden Brane

In summary, the stress-energy tensor can take different forms depending on the model being used, and it is important to carefully consider its components and their meanings in the context of the specific model.
  • #1
alejandrito29
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In a space time [tex]5D[/tex], the action for the brane [tex]4D[/tex] is:

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

In the Randall Sundrum the action for the hidden brane is:
[tex] V_0\int dx^4 \sqrt{-h}[/tex], where [tex]V_0[/tex] is the tension on the brane hidden.

follow the stress energy tensor

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

In other paper, where [tex]T_{MN}[/tex] is not diagonal, for example in the friedman equation in http://arxiv.org/abs/hep-th/0303095v1 (page 6)...

[tex] T_{00}= -\rho \delta(\phi)[/tex]
[tex] T_{ii}= p \delta(\phi)[/tex]
the other component are zero.

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

If , i use other embedding my energy stress tensor is
[tex] T_{00}= - \delta(\phi)[/tex]
[tex] T_{ii}= \delta(\phi)[/tex]
[tex] T_{0 \phi}= \delta(\phi)[/tex]
[tex] T_{\phi \phi}= \delta(\phi)[/tex]

¿can i to multiply the each component of the stress tensor by differents constants?...for example:
[tex] T_{00}= - k_1 \delta(\phi)[/tex]
[tex] T_{ii}= k_2 \delta(\phi)[/tex]
[tex] T_{0 \phi}= k_3 \delta(\phi)[/tex]
[tex] T_{\phi \phi}= k_4 \delta(\phi)[/tex]
 
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  • #2


I would like to start by clarifying that the action for the brane 4D in a 5D space-time is given by the first equation, \int dx^4 \sqrt{-h}. This is a standard action for a brane in a higher dimensional space-time and is used in various models, such as the Randall-Sundrum model.

Moving on to the discussion about the stress-energy tensor, the equations provided in the forum post seem to be derived from different models and situations. In the Randall-Sundrum model, the hidden brane has a tension, represented by V_0, which is included in the action. This leads to the form of the stress-energy tensor provided in the forum post.

However, in the other paper mentioned, the stress-energy tensor is not diagonal and has different components, with \rho representing energy density and p representing pressure. It is important to note that the form of the stress-energy tensor depends on the specific model and situation being studied. So, in answer to the question about multiplying the components of the stress-energy tensor by different constants, it would depend on the specific model and its underlying assumptions.

In general, as a scientist, it is important to carefully consider the assumptions and equations used in a particular model and to ensure that they are consistent and applicable to the situation being studied. It is also important to properly interpret and analyze the results obtained from the model.
 

1. What is the Stress Energy Tensor in 5D Space-Time?

The Stress Energy Tensor in 5D Space-Time is a mathematical representation of the energy and momentum density of a system in five-dimensional space-time. It includes components for both matter and energy, and is used to describe the distribution and flow of these quantities within a given space.

2. How is the Stress Energy Tensor related to Branes and Hidden Branes?

The Stress Energy Tensor is used in the formulation of the Action for Brane and Hidden Brane, which is a mathematical framework for studying the behavior of branes and hidden branes in five-dimensional space-time. The tensor is an essential component of this action, as it describes the energy and momentum of the branes and their interactions with the surrounding space.

3. What is the significance of studying the Stress Energy Tensor in 5D Space-Time?

Studying the Stress Energy Tensor in 5D Space-Time is important for understanding the behavior and dynamics of systems in higher dimensions. It is particularly relevant in theories of gravity and cosmology, where the presence of extra dimensions can have a significant impact on the behavior of matter and energy.

4. How is the Stress Energy Tensor in 5D Space-Time calculated?

The Stress Energy Tensor is calculated using mathematical equations that take into account the various components of matter and energy in a given system. These equations can be derived from the action for brane and hidden brane, and ultimately, from the fundamental laws of physics such as general relativity and quantum mechanics.

5. Are there any practical applications of the Stress Energy Tensor in 5D Space-Time?

While the concept of higher-dimensional space-time may seem abstract, the study of the Stress Energy Tensor in 5D Space-Time has practical applications in areas such as cosmology and theoretical physics. It allows scientists to develop and test theories of gravity and the behavior of matter and energy in higher dimensions, which can ultimately lead to a deeper understanding of the fundamental laws of the universe.

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