PhyPsy
Jan31-12, 02:35 PM
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.
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.