1. ### I What does the j means in this notation?

This section of Introduction to Electrodynamics by Griffiths, section 8.2.2 (page 363), is talking about the Maxwell's Stress Tensor. I do not quite understand what the j means on the left = sign (for either of the two representations) in the attached figure highlighted in yellow color. I have...
2. ### I Simpler name for the conserved property of spacetime?

If we have come to realize that energy conservation is not the most general conservation law in our spacetime, isn't it odd that we don't have a simple name for the "real deal"? I bumped into this thought through Noether's theorem, which relates symmetries in fields to conservation of all kinds...
3. ### I Definition of stress-energy tensor

Hello! Why is the stress energy tensor defined as a (2 0) tensor? I understand that it needs 2 one-forms as arguments, but using the metric, can't we bring it to (1 1) or (0 2)? So is there is any physical or mathematical reason why it is defined as (2 0), or it is equally right to define it as...
4. ### A What is the coordinate free stress-energy-momentum tensor

Without regard to a coordinate system (I only wish to consider special relativity) the stress-energy-momentum tensor defines a linear transformation from a 4-vector to a 4-vector. Let T be the linear transformation then b = T(a), a and b are 4-vectors. What is the physical meaning of a and b...
5. ### Heuristic Evaluation of Stress-Energy Tensor

I've been reading through Schutz's A First Course in General Relativity, and my solution to a particular problem has got me wondering if I'm being careful enough in my approach. The problem states: Show that, in the rest frame ##\mathcal{O}## of a star of constant luminosity ##L## (total energy...