The nuclear force is not simple, however, since it depends on the nucleon spins, has a tensor component, and may depend on the relative momentum of the nucleons.
12.
In a stationary spacetime, the metric tensor components, g _ { \ mu \ nu }, may be chosen so that they are all independent of the time coordinate.
13.
As stated above, the quantum analog of this is the partial trace operation, which can be viewed as projection onto a tensor component . " End of note"
14.
The nuclear force also has a tensor component which depends on the interaction between the nucleon spins and the angular momentum of the nucleons, leading to deformation from a simple spherical shape.
15.
As to the Ricci tensor components \ scriptstyle { R _ a ^ 0 }, \ scriptstyle { R _ a ^ 3 }, by this calculation they are identically zero.
16.
This is clearly not enough, as there are only 14 equations ( 10 from the field equations and 4 from the continuity equation ) for 20 unknowns ( 10 metric components and 10 stress energy tensor components ).
17.
Since there are different choices of metric with different metric signatures ( signs along the diagonal elements, i . e . tensor components with equal indices ), the name and signature is usually indicated to prevent confusion.
18.
For notational simplicity one usually drops the round brackets around the indices, recognizing that they can both label a set of ( co ) vectors and tensor components with respect to the ( co ) tetrad defined by these ( co ) vectors.
19.
Mathematically, this specificity is related to the fact that for the homogeneous space geometry discussed here, the Ricci tensor components \ scriptstyle { R _ \ alpha ^ 0 } are identically zeros and therefore the Einstein equations would not allow movement of matter ( which gives non-zero stress energy-momentum tensor components \ scriptstyle { T _ \ alpha ^ 0 } ).
20.
Mathematically, this specificity is related to the fact that for the homogeneous space geometry discussed here, the Ricci tensor components \ scriptstyle { R _ \ alpha ^ 0 } are identically zeros and therefore the Einstein equations would not allow movement of matter ( which gives non-zero stress energy-momentum tensor components \ scriptstyle { T _ \ alpha ^ 0 } ).
