There are several papers that study the implications of closed timelike curves (CTCs) to quantum complexity. In 2008, Aaronson and Watrous published their famous paper on this topic which shows that certain forms of time travel can make classical and quantum computing equivalent i.e. quantum computers provide no computational advantage if they can send information to the past through closed-timelike curves.
The abstract clearly says that closed timelike curves are not known to exist. So why exactly are complexity theorists interested in this topic? Does the study of CTCs provide some non-trivial insight into the fundamentals of complexity theory?
Are there any other world lines that are popularly studied in the context of complexity theory? If yes, why? If not, why not (and then what's so special about CTCs)?
I haven't really gotten around to working through the CTC papers, but I'm trying to get an idea of the "big picture" here, so as to understand the motivation behind studying this topic.
Note: I previously asked about this on Quantum Computing SE, in the context of quantum information theory, but here I'm specifically trying to view it through the lenses of a complexity theorist or computer scientist.