Wormholes
There are two parts to the study of traversable wormholes. Firstly there is the question of finding a solution to the equations of general relativity which represents a wormhole. Secondly there is the study of the properties of such objects, and in particular how they can lead to time travel without paradoxes.
Black Holes, Wormholes and Time Machines by
Jim Al-Khalili gives an easy to understand introduction to general relativity, but doesn't go into the questions of consistency. If you want a non-technical book which looks at both parts then I would recommend
In search of the edge of time by
John Gribbin.
For a book on time travel that has plenty about wormholes you could look at Time Travel in Einstein's Universe by J. Richard Gott. For a more philosophical viewpoint, including the self-consistency question, there's The River of Time by Igor Novikov , who has been active in the academic research into wormholes, as has Kip Thorne whose book Black holes and time warps also has a chapter on wormholes and self-consistency of time travel. Indeed it was Thorne who was approached by Carl Sagan when writing his science fiction book Contact, and it was this which stimulated recent research into traversable wormholes. There is a chapter on wormholes in Carl Sagan's universe by Yervant Terzian and Elizabeth Bilson.
Textbook
There's really only one book if you want to get into the mathematical study of wormholes, that is
Lorentzian Wormholes by
Matt Visser. This is well presented, and so worth looking at, even if you can't follow all of the mathematics.
Papers and online references
The idea of wormholes in space has been around for some time. Early solutions of Einstein's equations suggested the Einstein - Rosen bridge, but this could not be traversed. Theoretical interest revived in the late 1980's, in particular with the paper.
Wormholes in spacetime and their use for interstellar travel ; Morris MJ and Thorne KS, Am J Phys 56, 395 (1988) . The simulation on this website is based on the consistency calculations in
Billiard Balls in Wormhole spacetimes with closed timelike curves. Classical theory; Echeverria F, Klinkhammer G, Thorne K.S. Physical Review D 44 (4) 1991, pp.1077-1099. The substantial interest in the mathematics of wormholes continued up until the mid 1990's. For more references I would suggest you look at one of the later papers such as
Time machines and the Principle of Self-Consistency as a consequence of the Principle of Stationary Action (II): the Cauchy problem for a self-interacting relativistic particle; A. Carlini, I.D. Novikov Int.J.Mod.Phys. D5 (1996) 445-480.
TIME MACHINES IN PHYSICS has references to a many more papers on this and related subjects.
