Relativistic angular momentum can be compactly abbreviated in tensor index notation where the indices "i" and "j" take the values 1, 2, 3. On the other hand, the components can be systematically displayed fully in a 3 × 3 antisymmetric matrix This quantity is additive, and for an isolated system, the total angular momentum of a system is conserved. In classical mechanics, the three-dimensional quantity for a particle of mass "m" moving with velocity u has the dimensions of "mass moment" – length multiplied by mass. It is related to the boost (relative velocity) of the centre of mass (COM) of the particle
Komar mass knowledge of the components of formula_37, we can see that K = formula_3. If we chose our spatial coordinates so that we have a locally Minkowskian metric formula_39 we know that With these coordinate choices, we can write our Komar integral as While we can't choose a coordinate system to make a curved space-time globally Minkowskian, the above formula provides some insight into the meaning of the Komar mass formula. Essentially, both energy and pressure contribute to the Komar mass. Furthermore, the contribution of local energy and mass to the system mass is multiplied by the local "red shift" factor