I'm a hobbyist reader/student looking for some reading material on the predicted effects of tachyons and black holes (or other ultra-high gravity wells). Are there any good links or references people can recommend?
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You don't say how much physics and maths you already know. If you're prepared to put in a bit of effort (well, quite a lot of effort really :-) you can get a good understanding of general relativity without having to become an expert. This will make it much clearer what black holes are and why they are so interesting. Without putting in the effort I'm afraid you're stuck at the Discovery Channel level.
If you're interested I strongly recommend "A first course in general relativity" by Bernard F Schutz. This won't make you an expert in GR but it will give you a really good understand of the physics behind it. Another excellent book is "The cosmic frontiers of general relativity" by William J Kaufmann, though I think this is out of print so you'll have to buy second hand. The Kaufmann is less mathematical, so maybe read it first.
I don't think there is much that is interesting about tachyons since, unlike black holes, they don't exist.