If the spacetime continuum is a fabric, then can a hole, gash or rip be broken into it?

Today in my physics cl which does absolutely nothing I asked my teacher to describe the spacetime continuum to me and he said it was basically a fabric or canvas stretched out. He explained how gravity worked under this context and how light can even be affected by gravity, if it can be manipulated like a fabric in such a sense, then can it be torn or pierced like a fabric? If so how? Are there any resources on this subject that I should look over? thank you ahead of time