Looking for a stress analogue in E&M

  • Thread starter jfy4
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  • #1
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Main Question or Discussion Point

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. Im 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 doesnt look like E&M has a source for influence on the fields from what would be analogues for stress. Any comments on this?
 

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  • #2
Stingray
Science Advisor
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The thing you're looking for is called the Maxwell stress tensor. More generally, the full stress-energy tensor for an electromagnetic field [itex]F_{ab}[/itex] is
[tex]
T_{ab} = \frac{1}{4\pi} ( F_{a}{}^{c} F_{bc} - \frac{1}{4} g_{ab} F_{cd} F^{cd} )
[/tex]
Purely spatial components of this do not necessarily vanish.
 
  • #3
649
3
The thing you're looking for is called the Maxwell stress tensor. More generally, the full stress-energy tensor for an electromagnetic field [itex]F_{ab}[/itex] is
[tex]
T_{ab} = \frac{1}{4\pi} ( F_{a}{}^{c} F_{bc} - \frac{1}{4} g_{ab} F_{cd} F^{cd} )
[/tex]
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 [tex]T^{ij}[/tex] 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 "[tex]\dot{I}[/tex] density tensor" with the dot being the time derivative.

has anyone seen work related to this or have any suggestions or comments?
 
  • #4
Stingray
Science Advisor
671
1
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.
 
  • #5
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