Effective mass (solid-state physics) from both sides gives where is the th element of , is the th element of , and are the th and th elements of , respectively, and is the total energy of the particle according to the Planck–Einstein relation. The index is contracted by the use of Einstein notation (there is an implicit summation over ). Since Newton's second law uses the inertial mass (not the gravitational mass), we can identify the inverse of this mass in the equation above as the tensor This tensor expresses the change in group velocity due to a change in crystal momentum. Its
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