Interesting question. I'd do it roughly as follows.
Texture the black hole with the two images - but make sure the object is contained well within the ring texture. Then gradually expand the UV coordinates from their centre values, i.e. (U,V)=(0.5,05). That will make the texture appear to shrink towards the centre. You then need to reset the amount of shrinkage each time a ring coincides with the position of the previous one and repeat the same procedure - you'll need to work out when that happens with a bit of math and simple experimentation. You should then get the impression of concentric rings continually shrinking towards the centre. I would calculate the amount of shrinkage within DBPro and pass it as a constant each sync to the shader. Should be simpler and more efficient to do it that way rather than in the shader.
Making the other objects distort as they fall into the black hole is another matter.
revenant chaos Nice demo - but I wouldn't do it that way. The simplicity of your method is that you don't need the maths to get the shrinking effect. The downside is, as you say, that you need a specially constructed object. My method should work with a simple plain.
I'm interested in seeing how this turns out.
