Andy Weir's recent Project Hail Mary spins slower than the speed of light travel exactly like this.
Universe may be big, but (actually) not so much for the ones traveling. It's like it's calling to us..... dun dun dunnn.
If you're into GR and a fair bit studious you can learn more here.
If you're into my worst book spoiler ever up there you could check out Weir's book, >!but it's definitely about something else!<. It oozes Weir if you're into that style. :)
If you want to go down a more unconventional path there's always Gravitation. It's self contained and you'll be learning from the masters.
But I like studying other stuff. I’ve read all these books and done some exercises
https://www.amazon.com.br/Gravitation-Charles-W-Misner/dp/0691177791
https://www.amazon.com/First-Course-String-Theory-2nd/dp/0521880327
https://www.amazon.com/Geometry-Topology-Physics-Graduate-Student/dp/0750306068
https://www.amazon.com.br/Principles-Mathematical-Analysis-Walter-Rudin/dp/007054235X
https://www.amazon.com.br/Riemannian-Geometry-Manfredo-Perdigao-Carmo/dp/B09KXM4M7H
https://www.amazon.com.br/Quantum-Field-Theory-Standard-Model/dp/1107034736
https://www.amazon.com.br/Variational-Principles-Mechanics-Cornelius-Lanczos/dp/0486650677
https://www.amazon.com/Mechanics-Course-Theoretical-Physics-Landau/dp/0750628960
https://www.amazon.com/Classical-Theory-Fields-Theoretical-Physics/dp/0750627689
https://www.amazon.com.br/Superstring-Theory-Hardback-Set-Anniversary/dp/1107029112
https://www.amazon.com.br/Functional-Analysis-Frigyes-Riesz/dp/0486662896
https://www.amazon.com/Numerical-Methods-Partial-Differential-Equations/dp/1483235505
Since your objective seens to be general relativity, I suggest https://www.amazon.com.br/Gravitation-Charles-W-Misner/dp/0691177791, but if you're interested in a more mathematicaly rigorous approach, or need to study it deeper, like tensor fields, first study advanced linear algebra, real analysis and differential geometry, than I suggest reading using the book you're already familiar on advanced linear algebra or differential geometry, most probably one of then will cover tensor calculus.
Kerr. The ergosphere is actually important to the story. The concept and basic story was co-written by Kip Thorne. Yes, THAT Kip Thorne.
I am literally a physicist and I literally studied those things you're describing (the structure of accretion disks given some stochastic dynamics).
Again. We don't care about the why. We care about the how. And we already know how mass-energy causes spacetime curvature.
Read these, then we will have a discussion about the how of gravitational physics:
https://smile.amazon.com/Gravitation-Charles-W-Misner/dp/0691177791
https://smile.amazon.com/Introduction-Differential-Geometry-Curves-Surfaces/dp/1546735895