## 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.