EM stress-energy tensor

[Gatchaman]

Is it possible for an EM stress-energy tensor such as this:

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


\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}


so if Ex and Ey 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_solution


Perfect 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 Tzz 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 T0x and T0y components and Txy Tyx 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 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.

[Mentz114]

I've been looking into domain walls and d2-branes.
That's beyond my ken so I have to leave it to you.