Quadropole Formalism: Necessary Condition?

[mersecske]

v << c is the only necessary condition to use the formalism?

 

[Mentz114]

Contributions from higher moments fall off at 1/c² so for the v << c range you can forget them.

If you mean the quadrupole moment.

 

[WannabeNewton]

You also have to assume that the radiation being generated is pretty much traveling radially so that the space intervals in the retarded potential can simple be replaced by the radius and the quadrupole tensor can be defined in the normal way under the quadrupole approximation. Also, you ignore any r^-2 terms and the r^-1 terms that are not dominant in the slow motion approximation you mentioned.

 

[Meir Achuz]

You also need r>>d, where d is the size of the source,
and r>>lambda.
v<<c is also equivalent to lambda>>d.

 

[mersecske]

For v << c the system must have quadrupole to radiate.
For large velocities the quadrupole formalism is not good,
but this statement is still true?
Or it is possible to radiate without quadrupole moment?