Probably not. Things can get very weird.
For example, let us say that TODAY I could travel back in time. Say for example I go back in time TO BEFORE I WAS BORN and I kill my mother (sorry mom, but its just science!).
Then do you see the paradox?
This is called causality.... and that seems to be an important principle...
If I go back in time and kill my mother before I was born, then how is it that I am here NOW?????
Inside a black hole however, the laws of physics as we know them breakdown and its hard to say if time travel (in some form that does not violate causality) can be accomplished.
Very interesting business; perhaps in a few hundred years when we have a better understanding of cosmology and particle physics we will be able to investigate this issue in a meaningful way.
Today it's all science fiction.
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