Can an EM Stress-Energy Tensor Exist with Equal Sigma-Values?

[Gatchaman]

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} ?

 

[Mentz114]

I don't think so, because the Maxwell stress tensor is

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

so if E_x and E_y are non-zero then the \sigma_{xy} 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.

 

[Gatchaman]

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?

 

[Mentz114]

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 \partial_x\phi and \partial_y\phi

[Edit]my suggestion won't help because there will be a T_zz term.

 

[Gatchaman]

I don't think one exists.

How about an energy-momentum tensor? Perfect fluid with zz having no interaction with xx or yy components?

 

[Mentz114]

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 T_0x and T_0y components and T_xy T_yx components.

 

[Gatchaman]

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 T_0x and T_0y components and T_xy T_yx components.

I don't think you're correct. I've been looking into domain walls and d2-branes.

 

[Mentz114]

I've been looking into domain walls and d2-branes.

That's beyond my ken so I have to leave it to you.