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Closed timelike curve

Index Closed timelike curve

In mathematical physics, a closed timelike curve (CTC) is a world line in a Lorentzian manifold, of a material particle in spacetime that is "closed", returning to its starting point. [1]

47 relations: Black hole, BTZ black hole, Cauchy horizon, Cauchy surface, Causal structure, Causality, Causality conditions, Chronology protection conjecture, Closed timelike curve, Cosmic string, Covering space, Determinism, Dust solution, Einstein field equations, Event horizon, Exact solutions in general relativity, Free fall, Gödel metric, General relativity, Geodesic, Grandfather paradox, Internet Archive, J. Richard Gott, Kerr metric, Kurt Gödel, Light cone, Mathematical physics, Metric tensor (general relativity), Minkowski space, Misner space, My Brief History, Novikov self-consistency principle, Orbifold, Pseudo-Riemannian manifold, PSPACE, Quantum gravity, Rest frame, Roman ring, Spacetime, Speed of light, Stephen Hawking, Time travel, Timelike homotopy, Tipler cylinder, Van Stockum dust, Willem Jacob van Stockum, World line.

Black hole

A black hole is a region of spacetime exhibiting such strong gravitational effects that nothing—not even particles and electromagnetic radiation such as light—can escape from inside it.

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BTZ black hole

The BTZ black hole, named after Máximo Bañados, Claudio Teitelboim, and Jorge Zanelli, is a black hole solution for (2+1)-dimensional topological gravity with a negative cosmological constant.

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Cauchy horizon

In physics, a Cauchy horizon is a light-like boundary of the domain of validity of a Cauchy problem (a particular boundary value problem of the theory of partial differential equations).

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Cauchy surface

Intuitively, a Cauchy surface is a plane in space-time which is like an instant of time; its significance is that giving the initial conditions on this plane determines the future (and the past) uniquely.

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Causal structure

In mathematical physics, the causal structure of a Lorentzian manifold describes the causal relationships between points in the manifold.

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Causality

Causality (also referred to as causation, or cause and effect) is what connects one process (the cause) with another process or state (the effect), where the first is partly responsible for the second, and the second is partly dependent on the first.

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Causality conditions

In the study of Lorentzian manifold spacetimes there exists a hierarchy of causality conditions which are important in proving mathematical theorems about the global structure of such manifolds.

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Chronology protection conjecture

The chronology protection conjecture is a conjecture first proposed by Stephen Hawking which hypothesizes that the laws of physics are such as to prevent time travel on all but submicroscopic scales.

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Closed timelike curve

In mathematical physics, a closed timelike curve (CTC) is a world line in a Lorentzian manifold, of a material particle in spacetime that is "closed", returning to its starting point.

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Cosmic string

Cosmic strings are hypothetical 1-dimensional topological defects which may have formed during a symmetry breaking phase transition in the early universe when the topology of the vacuum manifold associated to this symmetry breaking was not simply connected.

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Covering space

In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below.

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Determinism

Determinism is the philosophical theory that all events, including moral choices, are completely determined by previously existing causes.

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Dust solution

In general relativity, a dust solution is a fluid solution, a type of exact solution of the Einstein field equation, in which the gravitational field is produced entirely by the mass, momentum, and stress density of a perfect fluid that has positive mass density but vanishing pressure.

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Einstein field equations

The Einstein field equations (EFE; also known as Einstein's equations) comprise the set of 10 equations in Albert Einstein's general theory of relativity that describe the fundamental interaction of gravitation as a result of spacetime being curved by mass and energy.

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Event horizon

In general relativity, an event horizon is a region in spacetime beyond which events cannot affect an outside observer.

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Exact solutions in general relativity

In general relativity, an exact solution is a Lorentzian manifold equipped with tensor fields modeling states of ordinary matter, such as a fluid, or classical nongravitational fields such as the electromagnetic field.

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Free fall

In Newtonian physics, free fall is any motion of a body where gravity is the only force acting upon it.

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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 (dust solution), and the second associated with a nonzero cosmological constant (see lambdavacuum solution).

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General relativity

General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.

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Geodesic

In differential geometry, a geodesic is a generalization of the notion of a "straight line" to "curved spaces".

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Grandfather paradox

The grandfather paradox is a paradox of time travel in which inconsistencies emerge through changing the past.

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Internet Archive

The Internet Archive is a San Francisco–based nonprofit digital library with the stated mission of "universal access to all knowledge." It provides free public access to collections of digitized materials, including websites, software applications/games, music, movies/videos, moving images, and nearly three million public-domain books.

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J. Richard Gott

John Richard Gott III (born February 8, 1947 in Louisville, Kentucky) is a professor of astrophysical sciences at Princeton University.

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Kerr metric

The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially-symmetric black hole with a spherical event horizon.

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Kurt Gödel

Kurt Friedrich Gödel (April 28, 1906 – January 14, 1978) was an Austrian, and later American, logician, mathematician, and philosopher.

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Light cone

In special and general relativity, a light cone is the path that a flash of light, emanating from a single event (localized to a single point in space and a single moment in time) and traveling in all directions, would take through spacetime.

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Mathematical physics

Mathematical physics refers to the development of mathematical methods for application to problems in physics.

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Metric tensor (general relativity)

In general relativity, the metric tensor (in this context often abbreviated to simply the metric) is the fundamental object of study.

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Minkowski space

In mathematical physics, Minkowski space (or Minkowski spacetime) is a combining of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded.

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Misner space

Misner space is an abstract mathematical spacetime, discovered by Charles Misner of the University of Maryland.

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My Brief History

My Brief History is a memoir published in 2013 by the English physicist Stephen Hawking.

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Novikov self-consistency principle

The Novikov self-consistency principle, also known as the Novikov self-consistency conjecture and Larry Niven's law of conservation of history, is a principle developed by Russian physicist Igor Dmitriyevich Novikov in the mid-1980s.

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Orbifold

In the mathematical disciplines of topology, geometry, and geometric group theory, an orbifold (for "orbit-manifold") is a generalization of a manifold.

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Pseudo-Riemannian manifold

In differential geometry, a pseudo-Riemannian manifold (also called a semi-Riemannian manifold) is a generalization of a Riemannian manifold in which the metric tensor need not be positive-definite, but need only be a non-degenerate bilinear form, which is a weaker condition.

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PSPACE

In computational complexity theory, PSPACE is the set of all decision problems that can be solved by a Turing machine using a polynomial amount of space.

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Quantum gravity

Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics, and where quantum effects cannot be ignored, such as near compact astrophysical objects where the effects of gravity are strong.

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Rest frame

In special relativity the rest frame of a particle is the coordinate system (frame of reference) in which the particle is at rest.

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Roman ring

In general relativity, a Roman ring (proposed by Matt Visser in 1997 and named after the Roman arch, a concept proposed by Mike Morris and Kip Thorne in 1988 and named after physicist Tom Roman) is a configuration of wormholes where no subset of wormholes is near to chronology violation, though the combined system can be arbitrarily close to chronology violation.

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Spacetime

In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum.

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Speed of light

The speed of light in vacuum, commonly denoted, is a universal physical constant important in many areas of physics.

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Stephen Hawking

Stephen William Hawking (8 January 1942 – 14 March 2018) was an English theoretical physicist, cosmologist, and author, who was director of research at the Centre for Theoretical Cosmology at the University of Cambridge at the time of his death.

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Time travel

Time travel is the concept of movement between certain points in time, analogous to movement between different points in space by an object or a person, typically using a hypothetical device known as a time machine.

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Timelike homotopy

On a Lorentzian manifold, certain curves are distinguished as timelike.

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Tipler cylinder

A Tipler cylinder, also called a Tipler time machine, is a hypothetical object theorized to be a potential mode of time travel—although results have shown that a Tipler cylinder could only allow time travel if its length were infinite or with the existence of negative energy.

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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.

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Willem Jacob van Stockum

Willem Jacob van Stockum (20 November 1910 – 10 June 1944) was a mathematician who made an important contribution to the early development of general relativity.

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World line

The world line (or worldline) of an object is the path that object traces in -dimensional spacetime.

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Closed Timelike Curve, Closed time-like, Closed time-like curve, Closed timelike curves, Closed timelike loop, Pseudo-photons, Timelike loop, Timelike topological feature, Timelike wormhole.

References

[1] https://en.wikipedia.org/wiki/Closed_timelike_curve

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