You might be interested in browsing through this site:
https://projectrho.com/public_html/rocket/
It talks about a lot of sci fi tropes from a hard science perspective, and goes over FTL specifically:
https://www.projectrho.com/public_html/rocket/fasterlight.php
It's kind of a downer site in some respects because it does a lot of "here's why your favorite sci fi series is unrealistic", but in that discussion there's a lot of looking at interesting tropes and concepts. There's also a good explainer for FTL specifically here:
https://www.physicsmatt.com/blog/2016/8/25/why-ftl-implies-time-travel