# Why shear stress components of the Stress Energy tensor not zero?

Hi,
I am having trouble understanding why Tij can be non-zero for i≠j. Tij is the flux of the i-th component of momentum across a surface of constant xj. Isn't the i-th component of momentum tangent to the surface of constant xj and therefore its flux across that surface zero? What am I missing here?

## Answers and Replies

Related Special and General Relativity News on Phys.org
pervect
Staff Emeritus
The principle axis theorem says that there are some basis vectors for which ##T^{ij}## is diagonal and hence ##T^{ij}## zero for i ##\neq## j, but the basis vectors are not necessarily aligned with the principle axes and thus in general the off-diagonal entries can be nonzero. Consider the analogous case of the 3x3 Newtonian moment of inertia tensor, for instance.

I don't understand your answer, pervect. Why would we express the components of four-momentum in a basis vectors not aligned with the coordinates that define the surfaces of constant xi??? I have not been able to find a word of warning to that effect in any text...

Bill_K