# Energy- momentum tensor of photon fluid/EM- field

1. Oct 19, 2012

### Lurian

Hey!

In cosmology the notion of a photon fluid is often used, i.e. a perfect fluid with the equation of state $P=\frac{\rho}{3}$ and the stress-energy- momentum tensor of a perfect fluid. On the other hand, a photon fluid is just an electromagnetic field with the well- known definition for its stress- energy- momentum tensor. Where is the connection between those tensors? Is the fluid's stress- energy tensor just the diagonalized version of the EM- stress- energy tensor? Or is the connection between these tensors not so obvious?

2. Oct 19, 2012

### Mentz114

The SET of incoherent radiation, and of an EM plane wave are different from each other and the SET of an electromagnetic field. Photons don't carry charge so the SET of an electric field/magnetic field is not relevant to the photons ( EM radiation) case.

An EM plane wave has the SET Tmn = σKaKb where Km is a null propagation vector giving the direction of the plane wave. The SET of incoherent radiation is not diagonal, see here http://en.wikipedia.org/wiki/Null_dust_solution.

The electro-vacuum solutions have a diagonal Einstein tensor so that's the closest to a perfect fluid of them. See http://en.wikipedia.org/wiki/Electrovacuum_solution.

Last edited: Oct 19, 2012
3. Oct 19, 2012

### bcrowell

Staff Emeritus
Example 3 in section 8.1 may be helpful: http://www.lightandmatter.com/html_books/genrel/ch08/ch08.html#Section8.1 [Broken] The formatting of the matrices is messed up in the html version, so use the pdf.

The x-t components of the stress-energy tensor flip their signs under a parity inversion, so they have to vanish for an isotropic photon gas. They don't vanish for a wave propagating in a certain direction.

Last edited by a moderator: May 6, 2017