Discussion Overview
The discussion revolves around calculating the eigenvalues of the electromagnetic tensor ##F_{ab}## and the stress-energy tensor ##T_{ab}##, exploring both the mathematical approach and the physical implications of these eigenvalues. The scope includes theoretical considerations and mathematical reasoning related to tensor properties.
Discussion Character
- Exploratory, Technical explanation, Debate/contested, Mathematical reasoning
Main Points Raised
- One participant suggests calculating the eigenvalues of ##F_{ab}## and ##T_{ab}## without using the characteristic polynomial, questioning their physical meaning.
- Another participant notes that the eigenvalues of a real antisymmetric matrix are imaginary and proposes computing the eigenvalues of its square as a potential method.
- A different participant challenges the notion of eigenvalues for the tensors, stating that ##T_{\mu\nu}## and ##F_{\mu\nu}## are (0,2) tensors and thus do not have eigenvalues in the traditional sense, although they acknowledge the possibility of manipulating indices using the metric.
- One participant shares links to external resources that may provide additional context or related information on the classification of electromagnetic fields.
Areas of Agreement / Disagreement
Participants express differing views on the applicability of eigenvalues to the tensors in question, with some arguing for their relevance and others contesting the definition of eigenvalues in this context. The discussion remains unresolved regarding the proper approach to calculating eigenvalues and their interpretation.
Contextual Notes
The discussion highlights the dependence on definitions of eigenvalues and the implications of tensor types, as well as the potential limitations in the mathematical treatment of these tensors.