- #1

Apashanka

- 429

- 15

At each ##\lambda## say tangent vector V and A be the two possible vectors of the tangent space.

where ##V=V^\mu e_\mu## and ##A=A^\nu e_\nu##, {e} are the basis vectors.

Now ## \nabla_A V=A^\mu \nabla_\mu(V^\nu e_\nu)=A^\mu(\nabla_\mu V^\nu)e_\nu+A^\mu V^\nu(\nabla_\mu e_\nu)##Now if ##\nabla_\mu V^\nu=0## then the covariant derivative is still not zero .

Similarly from the energy-momentum conservation ##\nabla_\mu T^{\mu \nu}=0 ## from this can we say that in general the covariant derivative of this energy --momentum is non-zero by just comparing to rank 1 tensor??

May be there is something wrong above (I apologise) as I am trying to learn these things...

Thank you