Why Gravitational Waves are Decomposed in Spin Weighted Spherical Harmonics

[Skhaaan]

Hi All,

Can someone tell me why gravitational waves are always decomposed in spin weighted spherical harmonics with spin weight -2 ?

I'm assuming you can hand wave the answer with something to do with the 'graviton' being a spin 2 particle but this isn't very satisfying to me.

Are there any other decompositions? Why not just regular spherical harmonics?

On a more basic level, why is it advantageous to decompose anything into spherical harmonics?
Is it just another analysis you can perform to get more insight into the physics such as what 'poles' there are.
i.e. mono, di, quad, etc...
Or is it also supposed to simplify the algebra too?

Many thanks in advance!

Sebastian

 

[PAllen]

It would help if you gave a reference to what you are referring to. At least in classical treatments of gravitational waves, most sources I've read simply do not do what you describe at all. For example:

http://relativity.livingreviews.org/Articles/lrr-2011-1/

makes no mention of the decomposition you refer to.

I'm suspecting there is a particular reference you are reading that raised questions. In such case, you should always provide such a reference so people can look at what you are talking about.

 

[Skhaaan]

Hi, thanks for the reply and advice.

Sorry I didn't supply a reference, I didn't realize
that this decomposition was not more common.
It is very common in Gravitational Wave analysis.

This link gives a definition of the spin weighted spherical harmonics
http://arxiv.org/abs/gr-qc/0511111

I worked with this decomposition a lot but never understood the reason
for performing this decomposition. So then I wanted to ask
what is the reason for performing spherical harmonic decomposition
in general.

Maybe I will post again and ask the more general question on spherical harmonic decomposition

Thanks