Understanding Physics with a Rank 4 Tensor Example

[SteDolan]

Hi,

Can somebody give me an example of a rank 4 tensor in physics?

Thanks.

 

[Bill_K]

Sure, one would be the Riemann curvature tensor R_ijkl that's used in general relativity.

 

[SteDolan]

Thanks.

It was an odd small part of an exam question when my module had only covered examples up to 3rd rank.

 

[orhit]

Third order nonlinear susceptibility is another example of 4th rank tensor.

 

[pmacias]

Sure, a common example of a rank 4 tensor in physics is the stress-energy tensor, which is used in Einstein's theory of general relativity to describe the distribution of matter and energy in spacetime. This tensor has 4 indices and describes the stress and momentum in a given region of spacetime. Another example is the Riemann curvature tensor, which is used to describe the curvature of spacetime in general relativity. Both of these tensors play crucial roles in understanding the behavior of matter and energy in the universe and are essential tools in the study of physics.