# Christofel Symbols Tensors?

1. Mar 19, 2009

### Karl G.

I'm sort of confused about Christofel symbols being called tensors. I thought that to be considered a tensor, the tensor had to obey the standard component transformation law. For example: Ga'b' = Lca'Ldb'Gcd
But the Christofel symbols don't obey this transformation law; their components transform in a different way (I would like to show it, but I don't know how; see exercise 10.3 of MWT).
What gives?

2. Mar 19, 2009

### cristo

Staff Emeritus
No, Christoffel symbols are not tensors.

3. Mar 19, 2009

### Karl G.

Oh ... thought they were

4. Mar 20, 2009

### Mentz114

Christoffel symbols make the covariant derivative a tensor. Try transforming one.

5. Mar 20, 2009

### dx

I haven't seen a single book on GR which introduces the Christoffel symbols without immediately pointing out that they're not tensors.

6. Mar 21, 2009

### samalkhaiat

They transform inhomogeneously under general coordinates transformations, i.e., not tensors. However, the inhomogeneous term in the transformation law vanishes if the coordinate transformations are LINEAR. So, they do transform as tensors with respect to all linear coordinate transformations.

sam