I Calculate Eigenvalues of Electromagnetic & Stress-Energy Tensors

ergospherical
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How can we (as nicely as possible... i.e. not via characteristic polynomial) calculate the eigenvalues of ##F_{ab} = \partial_a A_b -\partial_b A_a## and ##T_{ab} = F_{ac} {F_b}^c- (1/4) \eta_{ab} F^2 ## and what is their physical meaning?
 
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I mean, first of all you would have to define what you mean by "eigenvalues". The entire concept of an eigenvalue is that you have an operator from a vector space to itself. As such, neither ##T_{\mu\nu}## or ##F_{\mu\nu}## have eigenvalues because they are (0,2) tensors. You can, of course, raise and lower an index using the metric if you have one, but then you no longer have a symmetric or anti-symmetric matrix.
 
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