Editing Tipler cylinder (section)

== Discovery ==
The Tipler cylinder was discovered as a solution to the equations of general relativity by [[Willem Jacob van Stockum]]<ref name="stockum">{{cite journal | first = Willem Jacob | last = van Stockum | author-link = Willem Jacob van Stockum | url = http://www.lorentz.leidenuniv.nl/history/stockum/Proc_R_Soc_Edinb_57_135_1937.jpg | title = The Gravitational Field of a Distribution of Particles Rotating about an Axis of Symmetry | year = 1936 | journal = Proceedings of the Royal Society of Edinburgh}}</ref> in 1936 and [[Kornel Lanczos]]<ref name="lanczos">{{cite journal | first = Kornel | last = Lanczos | author-link = Kornel Lanczos | doi = 10.1023/A:1010277120072 | title = On a Stationary Cosmology in the Sense of Einstein's Theory of Gravitation | orig-year = 1924 | date = 1997 | journal = General Relativity and Gravitation | publisher = Springland Netherlands | volume = 29 | issue = 3 | pages = 363–399| s2cid = 116891680 }}</ref> in 1924, but not recognized as allowing [[closed timelike curves]]<ref name="Earman1">{{cite book | last = Earman | first = John | title = Bangs, Crunches, Whimpers, and Shrieks: Singularities and Acausalities in Relativistic Spacetimes | publisher = Oxford University Press |date= 1995 | pages = 21 | isbn = 0-19-509591-X}}</ref> until an analysis by [[Frank Tipler]]<ref name="tipler paper">{{cite journal | first=Frank | last=Tipler | author-link = Frank J. Tipler | url=http://www.geocities.com/theophysics/tipler-rotating-cylinders.pdf | title=Rotating Cylinders and the Possibility of Global Causality Violation | journal = Physical Review D | volume = 9 | year=1974 | pages = 2203–2206 | doi=10.1103/PhysRevD.9.2203|archive-url=https://www.webcitation.org/5knqUI8MU?url=http://www.geocities.com/theophysics/tipler-rotating-cylinders.pdf|archive-date=2009-10-26| url-status=dead |bibcode = 1974PhRvD...9.2203T | issue=8 }} Available in [[Graphics Interchange Format|GIF]] format here: pages [http://www.vialattea.net/curvatura/articoli/t1.gif 1], [http://www.vialattea.net/curvatura/articoli/t2.gif 2], [http://www.vialattea.net/curvatura/articoli/t3.gif 3] and [http://www.vialattea.net/curvatura/articoli/t4.gif 4]. See also [http://adsabs.harvard.edu/abs/1974PhRvD...9.2203T here].</ref> in 1974. Tipler showed in his 1974 article "Rotating Cylinders and the Possibility of Global Causality Violation"<ref name="cylinder">{{cite journal | first = Frank J. | last = Tipler | author-link = Frank J. Tipler | url = https://journals.aps.org/prd/pdf/10.1103/PhysRevD.9.2203 | title = Rotating cylinders and the possibility of global causality violation* | journal = Physical Review D | year = 1974 | volume = 9 | issue = 8 | pages = 2203–2206 | doi = 10.1103/PhysRevD.9.2203 | bibcode = 1974PhRvD...9.2203T | url-access = subscription }}</ref> that in a [[spacetime]] containing a "sufficiently large rotating [[cylinder (geometry)|cylinder]]" spinning around its axis, the cylinder should create a [[frame-dragging]] effect. This frame-dragging effect warps spacetime in such a way that the [[light cone]]s of objects in the cylinder's proximity become tilted, so that part of the light cone then points backwards along the time axis on a [[spacetime diagram]]. Therefore, a [[spacecraft]] accelerating sufficiently in the appropriate direction can travel backwards through time along a [[closed timelike curve]].<ref name="tipler paper" />

CTCs are associated, in [[pseudo-Riemannian manifold|Lorentzian manifolds]] which are interpreted physically as spacetimes, with the possibility of causal anomalies such as a person going back in time and [[Grandfather paradox|potentially shooting their own grandfather]], although paradoxes might be avoided using some constraint such as the [[Novikov self-consistency principle]]. They appear in some of the most important exact solutions in general relativity, including the [[Kerr metric|Kerr vacuum]] (which models a [[rotating black hole]]) and the [[van Stockum dust]] (which models a cylindrically symmetrical configuration of rotating pressureless fluid or [[dust solution|dust]]).