Looking for a stress analogue in E&M

[jfy4]

Hello,

I was wondering if anyone has heard of or seen any work done into looking for what would be the analogue of stress in General Rel. for E&M. I am not talking about actual stress but the analogue to it. In the flat space metric with perturbations, linearized gravity begins to have close resemblance with E&M, save for the stress tensor. the densities and the currents are both analogues, however it doesn't look like E&M has a source for influence on the fields from what would be analogues for stress. Any comments on this?

 

[Stingray]

The thing you're looking for is called the Maxwell stress tensor. More generally, the full stress-energy tensor for an electromagnetic field $F_{ab}$ is
$$T_{ab} = \frac{1}{4\pi} ( F_{a}{}^{c} F_{bc} - \frac{1}{4} g_{ab} F_{cd} F^{cd} )$$
Purely spatial components of this do not necessarily vanish.

 

[jfy4]

The thing you're looking for is called the Maxwell stress tensor. More generally, the full stress-energy tensor for an electromagnetic field $F_{ab}$ is
$$T_{ab} = \frac{1}{4\pi} ( F_{a}{}^{c} F_{bc} - \frac{1}{4} g_{ab} F_{cd} F^{cd} )$$
Purely spatial components of this do not necessarily vanish.

Unfortunately I was trying to avoid this confusion, but the Maxwell stress tensor is stress. I am looking for the analogue if there is one. I can see the similarities between GR and E&M from there sources for influence. Mainly energy density vs charge density, and energy flux/momentum density vs current density, but then there is $$T^{ij}$$ which is the stress tensor in GR and which there appears to be no analogue in E&M. To me it seems like it would be a tensor of sort named "Current flux tensor" or "$$\dot{I}$$ density tensor" with the dot being the time derivative.

has anyone seen work related to this or have any suggestions or comments?

 

[Stingray]

Ah, ok. I misunderstood you.

There is no analog of stress that acts as a source in electromagnetism. Gravity is described by a symmetric rank 2 tensor (the metric), and electromagnetism by a rank 1 tensor (the vector potential). The former requires a more complicated source structure than the latter.

 

[heldervelez]

try here
A.26 Electromagnetism versus Elasticity
in the monograph
Elements for Physics
Quantities, Qualities, and Intrinsic Theories
by Albert Tarantola
download here:
http://www.ipgp.fr/~tarantola/Files/Professional/Books/index.html