Exploring the Possibility of an EM Stress-Energy Tensor with Equal Sigma-Values

In summary, the conversation discusses the possibility of an EM stress-energy tensor with equal \sigma_{xx} and \sigma_{yy} components. However, it is concluded that such a tensor does not exist, as all fields have a non-zero zz component and point particles have additional components as well. The possibility of a perfect fluid solution with a diagonal energy-momentum tensor is also considered, but ultimately dismissed. The conversation also mentions the Nordstrom-Reissner solution and the potential use of a scalar field, but it is determined that neither of these options would provide a solution with the desired properties.
  • #1
Gatchaman
25
0
Is it possible for an EM stress-energy tensor such as this:

[PLAIN]http://www3.telus.net/public/kots1906/emtensor.jpg

to exist, where \sigma_{xx} = \sigma_{yy} ?
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
I don't think so, because the Maxwell stress tensor is

[tex]
\sigma_{ij} = \epsilon_0 E_i E_j + \frac{1}
{{\mu _0 }}B_i B_j - \frac{1}
{2}\left( {\epsilon_0 E^2 + \frac{1}
{{\mu _0 }}B^2 } \right)\delta _{ij}
[/tex]

so if Ex and Ey are non-zero then the [itex]\sigma_{xy}[/itex] must be present.

But, there are electro-vacuum solutions of the EFE where the SET is diagonal so it may be worth looking that up.
 
  • #3
Nordstrom-Reissner solution? I looked, but couldn't figure it out.

Would a perfect fluid solution exist with diag(\rho, p, p, 0) you think?
 
  • #4
Gatchaman said:
Nordstrom-Reissner solution? I looked, but couldn't figure it out.

Would a perfect fluid solution exist with diag(\rho, p, p, 0) you think?

Electrovac is here
http://en.wikipedia.org/wiki/Electrovacuum_solutionPerfect fluid is isotropic. You could try a scalar field where the Lagrangian depends only on [itex]\partial_x\phi[/itex] and [itex]\partial_y\phi[/itex]

[Edit]my suggestion won't help because there will be a Tzz term.
 
Last edited:
  • #5
I don't think one exists.

How about an energy-momentum tensor? Perfect fluid with zz having no interaction with xx or yy components?
 
  • #6
No, I don't think there is any EMT that corresponds to your example. A field will always have a zz component, and a point particle will have T0x and T0y components and Txy Tyx components.
 
  • #7
Mentz114 said:
No, I don't think there is any EMT that corresponds to your example. A field will always have a zz component, and a point particle will have T0x and T0y components and Txy Tyx components.

I don't think you're correct. I've been looking into domain walls and d2-branes.
 
  • #8
Gatchaman said:
I've been looking into domain walls and d2-branes.
That's beyond my ken so I have to leave it to you.
 

Related to Exploring the Possibility of an EM Stress-Energy Tensor with Equal Sigma-Values

1. What is an EM Stress-Energy Tensor with Equal Sigma-Values?

An EM Stress-Energy Tensor with Equal Sigma-Values is a mathematical representation of the stress and energy associated with electromagnetic fields. It describes the distribution of energy and momentum in an electromagnetic field and is an important concept in the study of electromagnetism.

2. Why is it important to explore the possibility of an EM Stress-Energy Tensor with Equal Sigma-Values?

Exploring the possibility of an EM Stress-Energy Tensor with Equal Sigma-Values can help us better understand the behavior of electromagnetic fields and how they interact with matter. This knowledge can have practical applications in various fields such as telecommunications, electronics, and energy production.

3. How is an EM Stress-Energy Tensor with Equal Sigma-Values calculated?

An EM Stress-Energy Tensor with Equal Sigma-Values is calculated using mathematical equations that take into account the electric and magnetic fields, as well as their derivatives. These calculations can be complex and require advanced mathematical techniques.

4. What are the potential implications of discovering an EM Stress-Energy Tensor with Equal Sigma-Values?

The discovery of an EM Stress-Energy Tensor with Equal Sigma-Values could have significant implications for our understanding of electromagnetism and its role in the universe. It could also lead to advancements in technology and energy production, as well as furthering our understanding of the fundamental laws of physics.

5. Are there any current experiments or studies being done on the EM Stress-Energy Tensor with Equal Sigma-Values?

Yes, there are ongoing experiments and studies being conducted to explore the possibility of an EM Stress-Energy Tensor with Equal Sigma-Values. These include theoretical research, computer simulations, and experiments using advanced equipment such as particle accelerators. However, further research and experimentation are needed to confirm the existence of such a tensor and fully understand its properties and implications.

Similar threads

I Obtaining the matter Lagrangian from the stress energy tensor
    • Special and General Relativity
Replies
11
Views
964
I Move Stress-Energy tensor to the left side of EFE?
    • Special and General Relativity
Replies
2
Views
190
I Question about Stress-Energy Tensor: A First Course in GR
    • Special and General Relativity
Replies
8
Views
1K
B Special Cases of Stress-Energy Tensor in GR
    • Special and General Relativity
Replies
10
Views
1K
I Diagonal Matrix of Stress-Energy Tensor: Why?
    • Special and General Relativity
Replies
17
Views
2K
A How Does Linear Framedragging Affect Parallel Moving Masses in Flat Spacetime?
    • Special and General Relativity
Replies
11
Views
1K
I Understanding the Stress-Energy Tensor in Special Relativity
    • Special and General Relativity
Replies
4
Views
746
A Stress-energy tensor of a rotating rod
    • Special and General Relativity
Replies
21
Views
2K
A MTW Gravitation: Exercise 5.1 | Beginner GR Stress-Energy Tensor Symmetry
    • Special and General Relativity
Replies
15
Views
1K
A Exploring the Stress-Energy Tensor of a Perfect Fluid
    • Special and General Relativity
Replies
3
Views
971

Hot Threads

Recent Insights

Back
Top