Where matter slows light, is spacetime affected?

Hi Naked Scientists, A little knowledge is a dangerous thing. I have been reading Dr Brian Cox's excellent book Why E=MC^2, which introduces spacetime and special relativity, with my 11 year old son. So far I have been able to answer most questions, and I have certainly learnt many things by reading it with him and having to explain things in a simpler way. One thing has me stumped about spacetime. I understand the time dimension has a constant c introduced to make the units similar to spacial dimensions, and this constant ultimately becomes the speed of massless particles (light). This got me wondering what happens to spacetime in a situation where light is slowed down, for example when it goes through glass or water. Is spacetime warped in an analogous way to mass warping spacetime?
Thanks
Martin