# closed timelike curve

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closed timelike curve
A worldline that returns to its starting point.

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• Closed timelike curve — In mathematical physics, a closed timelike curve (CTC) is a worldline in a Lorentzian manifold, of a material particle in spacetime that is closed, returning to its starting point. This possibility was first raised by Kurt Gödel in 1949, who… …   Wikipedia

• Timelike homotopy — On a Lorentzian manifold, certain curves are distinguished as timelike. A timelike homotopy between two timelike curves is a homotopy such that each intermediate curve is timelike. No closed timelike curve (CTC) on a Lorentzian manifold is… …   Wikipedia

• Timelike simply connected — Suppose a Lorentzian manifold contains a closed timelike curve (CTC). No CTC can be continuously deformed as a CTC (is timelike homotopic) to a point, as that point would not be causally well behaved. Therefore, any Lorentzian manifold containing …   Wikipedia

• Timelike topological feature — No closed timelike curve (CTC) on a Lorentzian manifold can be continuously deformed as a CTC to a point, because Lorentzian manifolds are locally causally well behaved. Every CTC must pass through some topological feature which prevents it from… …   Wikipedia

• List of curve topics — This is a list of curve topics in mathematics. See also curve, list of curves, and list of differential geometry topics.*acnode *algebraic curve *arc *asymptote *asymptotic curve *Barbier s theorem *barycentric… …   Wikipedia

• Causal structure — This article is about the possible causal relationships among points in a Lorentzian manifold. For classification of Lorentzian manifolds according to the types of causal structures they admit, see Causality conditions. In mathematical physics,… …   Wikipedia

• Gödel metric — The Gödel metric is an exact solution of the Einstein field equations in which the stress energy tensor contains two terms, the first representing the matter density of a homogeneous distribution of swirling dust particles, and the second… …   Wikipedia

• Novikov self-consistency principle — The Novikov self consistency principle, also known as the Novikov self consistency conjecture, is a principle developed by Russian physicist Igor Dmitriyevich Novikov in the mid 1980s to solve the problem of paradoxes in time travel, which is… …   Wikipedia

• Van Stockum dust — In general relativity, the van Stockum dust is an exact solution of the Einstein field equation in which the gravitational field is generated by dust rotating about an axis of cylindrical symmetry. Since the density of the dust is increasing with …   Wikipedia

• World line — In physics, the world line of an object is the unique path of that object as it travels through 4 dimensional spacetime.The concept of world line is distinguished from the concept of orbit or trajectory (such as an orbit in space or a trajectory… …   Wikipedia