How do I make a background radial shadow? {EXAMPLES INCLUDED}

[NBAmix]

I wanna produce a shadow like this, you can see the radial waves on the background. Can someone please explain on how to do it step by step? Thanks.

 

[Hoogle]

Several methods all basically leading to the same way method 1.

Gradient
Choose the Gradient tool select your 2 colours ie light gray to dark Gray
In the gradient style bar select radial
find center of your image click and drag to the outside of your image

Brush
Limited by the size of your document if it is to big beyond your max brush size then this method will not work But we are talking huge document sizes for this to happen.
Have your background colour the colour you want it to be
select brush tool and choose a round brush right click and drag the hardness slider to 0%
Select your lighter colour
Scale the brush up so that it is in the center of the document and just overlaps the document edges
then click repeatedly in the center of the document until you have the nice feathered effect.

Layer mask
Create a new layer and fill it with the colour black
apply a layer mask and paint in black
use the same method as brush
reduce the black layers opacity.

You can do the same technique with gradient on layer mask

There are literally 100s of ways of doing this from the simple ways described to using selection tools and feather
Actions that apply vignettes automatically etc.