Question

How is Infinitesimal coordinate transformation related to Lie derivatives?

Answer 1

I am reading the book "Gravitaion and Cosmology" by S. Weinberg. In section 10.9, while discussing Lie derivatives of tensors of different ranks, he makes a general comment:

The effect of an infinitesimal coordinate transformation on any tensor TT is that the new tensor equals the old tensor at the same coordinate point, plus the Lie derivative of the tensor.

Answer 2

The effect of an infinitesimal coordinate transformation on any tensor TT is that the new tensor equals the old tensor at the same coordinate point, plus the Lie derivative of the tensor.