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Misner Space
Misner space is an abstract mathematical spacetime, first described by Charles W. Misner. It is also known as the Lorentzian orbifold \mathbb^/\text. It is a simplified, two-dimensional version of the Taub–NUT spacetime. It contains a non-curvature singularity and is an important counterexample to various hypotheses in general relativity. Metric The simplest description of Misner space is to consider two-dimensional Minkowski space with the metric : ds^2= -dt^2 + dx^2, with the identification of every pair of spacetime points by a constant boost : (t, x) \to (t \cosh (\pi) + x \sinh(\pi), x \cosh (\pi) + t \sinh(\pi)). It can also be defined directly on the cylinder manifold \mathbb \times S with coordinates (t', \varphi) by the metric : ds^2= -2dt'd\varphi + t'd\varphi^2, The two coordinates are related by the map : t= 2 \sqrt \cosh\left(\frac\right) : x= 2 \sqrt \sinh\left(\frac\right) and : t'= \frac(x^2 - t^2) : \phi= 2 \tanh^\left(\frac\right) Causality Misner sp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spacetime
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why different observers perceive differently where and when events occur. Until the 20th century, it was assumed that the three-dimensional geometry of the universe (its spatial expression in terms of coordinates, distances, and directions) was independent of one-dimensional time. The physicist Albert Einstein helped develop the idea of spacetime as part of his theory of relativity. Prior to his pioneering work, scientists had two separate theories to explain physical phenomena: Isaac Newton's laws of physics described the motion of massive objects, while James Clerk Maxwell's electromagnetic models explained the properties of light. However, in 1905, Einstein based a work on special relativity on two postulates: * The laws of physics are invariant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles W
The F/V ''Charles W'', also known as Annie J Larsen, is a historic fishing schooner anchored in Petersburg, Alaska. At the time of its retirement in 2000, it was the oldest fishing vessel in the fishing fleet of Southeast Alaska, and the only known wooden fishing vessel in the entire state still in active service. Launched in 1907, she was first used in the halibut fisheries of Puget Sound and the Bering Sea as the ''Annie J Larsen''. In 1925 she was purchased by the Alaska Glacier Seafood Company, refitted for shrimp trawling, and renamed ''Charles W'' in honor of owner Karl Sifferman's father. The company was one of the pioneers of the local shrimp fishery, a business it began to phase out due to increasing competition in the 1970s. The ''Charles W'' was the last of the company's fleet of ships, which numbered twelve at its height. The boat was acquired in 2002 by the nonprofit Friends of the ''Charles W''. The boat was listed on the National Register of Historic Places in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lorentzian Manifold
In differential geometry, a pseudo-Riemannian manifold, also called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere nondegenerate. This is a generalization of a Riemannian manifold in which the requirement of positive-definiteness is relaxed. Every tangent space of a pseudo-Riemannian manifold is a pseudo-Euclidean vector space. A special case used in general relativity is a four-dimensional Lorentzian manifold for modeling spacetime, where tangent vectors can be classified as timelike, null, and spacelike. Introduction Manifolds In differential geometry, a differentiable manifold is a space which is locally similar to a Euclidean space. In an ''n''-dimensional Euclidean space any point can be specified by ''n'' real numbers. These are called the coordinates of the point. An ''n''-dimensional differentiable manifold is a generalisation of ''n''-dimensional Euclidean space. In a manifold it may only be possible to defi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orbifold
In the mathematical disciplines of topology and geometry, an orbifold (for "orbit-manifold") is a generalization of a manifold. Roughly speaking, an orbifold is a topological space which is locally a finite group quotient of a Euclidean space. Definitions of orbifold have been given several times: by Ichirô Satake in the context of automorphic forms in the 1950s under the name ''V-manifold''; by William Thurston in the context of the geometry of 3-manifolds in the 1970s when he coined the name ''orbifold'', after a vote by his students; and by André Haefliger in the 1980s in the context of Mikhail Gromov's programme on CAT(k) spaces under the name ''orbihedron''. Historically, orbifolds arose first as surfaces with singular points long before they were formally defined. One of the first classical examples arose in the theory of modular forms with the action of the modular group \mathrm(2,\Z) on the upper half-plane: a version of the Riemann–Roch theorem holds after the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taub–NUT Space
The Taub–NUT metric (,McGraw-Hill ''Science & Technology Dictionary'': "Taub NUT space" ) is an exact solution to Einstein's equations. It may be considered a first attempt in finding the metric of a spinning black hole. It is sometimes also used in homogeneous but anisotropic cosmological models formulated in the framework of general relativity. The underlying Taub space was found by , and extended to a larger manifold by , whose initials form the "NUT" of "Taub–NUT". Taub's solution is an empty space solution of Einstein's equations with topology R×S3 and metric (or equivalently line element) :g =-dt^2/U(t) + 4l^2U(t)(d\psi+ \cos\theta d\phi)^2+(t^2+l^2)(d\theta^2+(\sin\theta)^2d\phi^2) where :U(t)=\frac and ''m'' and ''l'' are positive constants. Taub's metric has coordinate singularities at U=0, t=m+(m^2+l^2)^, and Newman, Tamburino and Unti showed how to extend the metric across these surfaces. When Roy Kerr developed the Kerr metric The Kerr metric or Kerr geom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metric (mathematics)
In mathematics, a metric space is a set together with a notion of ''distance'' between its elements, usually called points. The distance is measured by a function called a metric or distance function. Metric spaces are the most general setting for studying many of the concepts of mathematical analysis and geometry. The most familiar example of a metric space is 3-dimensional Euclidean space with its usual notion of distance. Other well-known examples are a sphere equipped with the angular distance and the hyperbolic plane. A metric may correspond to a metaphorical, rather than physical, notion of distance: for example, the set of 100-character Unicode strings can be equipped with the Hamming distance, which measures the number of characters that need to be changed to get from one string to another. Since they are very general, metric spaces are a tool used in many different branches of mathematics. Many types of mathematical objects have a natural notion of distance and t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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). One side of the horizon contains closed space-like geodesics and the other side contains closed time-like geodesics. The concept is named after Augustin-Louis Cauchy. Under the averaged weak energy condition (AWEC), Cauchy horizons are inherently unstable. However, cases of AWEC violation, such as the Casimir effect caused by periodic boundary conditions, do exist, and since the region of spacetime inside the Cauchy horizon has closed timelike curves it is subject to periodic boundary conditions. If the spacetime inside the Cauchy horizon violates AWEC, then the horizon becomes stable and frequency boosting effects would be canceled out by the tendency of the spacetime to act as a divergent lens. Were this conjecture to be shown empirically true, it would provide a counter-example to the strong ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
