# Eigenvectors of the EM stress-energy tensor

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• Creedence
In summary, the EM stress-energy tensor is a 4x4 matrix that describes the distribution of energy and momentum in electromagnetic fields. Eigenvectors of this tensor represent the most significant directions of its effects and are useful in understanding the behavior of electromagnetic fields and simplifying calculations. They can be calculated using linear algebra techniques and have various real-world applications in physics, engineering, and image processing.
Creedence
TL;DR Summary
What do they mean?
My question is that what is the physical meaning of the EM stress-energy tensor's eigenvectors?
Thanks for the answers - Robert

I would think an eigenvector of a stress energy tensor to be that directed area for which the energy-momentum passing through is collinear with the area vector but I'm just guessing.

Isn't this rather provided by the eigenvectors of the ##3 \times 3## stress tensor alone and not the energy-momentum-stress tensor?

## 1. What are eigenvectors of the EM stress-energy tensor?

Eigenvectors of the EM stress-energy tensor are special vectors that represent the directions in which the tensor's components do not change when the tensor is multiplied by a scalar value. In other words, they are the directions in which the tensor has a constant magnitude and direction.

## 2. Why are eigenvectors of the EM stress-energy tensor important?

Eigenvectors of the EM stress-energy tensor play a crucial role in understanding the behavior of electromagnetic fields. They can help us identify the directions in which the fields are most stable, and can also be used to calculate important physical quantities such as the electric and magnetic field strengths.

## 3. How are eigenvectors of the EM stress-energy tensor calculated?

The calculation of eigenvectors of the EM stress-energy tensor involves solving a mathematical equation known as the characteristic equation. This equation involves the components of the tensor and requires the use of linear algebra techniques to find the solutions.

## 4. Can eigenvectors of the EM stress-energy tensor have complex values?

Yes, eigenvectors of the EM stress-energy tensor can have complex values. This is because the components of the tensor can also have complex values, and the characteristic equation can have complex solutions.

## 5. How are eigenvectors of the EM stress-energy tensor used in physics?

Eigenvectors of the EM stress-energy tensor are used in physics to analyze and understand the behavior of electromagnetic fields. They are also used in the study of general relativity, as they are closely related to the concept of spacetime curvature.

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