# Axial symmetry, non-rotating

1. Jan 31, 2012

### PhyPsy

I'm studying Bondi's work on gravitational radiation. He applied axial symmetry and reflection symmetry to a source of gravity. How is it that axial symmetry does not automatically imply reflection symmetry?

The assumption for axial symmetry is $\phi \rightarrow \phi'= \phi +$ constant

The assumption for reflection symmetry is $\phi \rightarrow \phi'= -\phi$

The first condition implies the second if the constant is $-2\phi$, so I don't see how the second assumption adds anything new to the source.

Also, I read that the second assumption prohibits the solution from rotating, but I don't see why this distinction needs to be made since it is invariant under any rotation.