- Weyl's postulate
In relativistic cosmology,

**Weyl's postulate**stipulates that in a fluid cosmological model, theworld line s of the fluid particles, which act as the source of the gravitational field and which are often taken to modelgalaxies , should be "hypersurface orthogonal". That is, the world lines should be everywhereorthogonal to a family of spatial hyperslices.Sometimes, the additional hypothesis is added that the world lines form timelike geodesics.

**Intuitive significance**In the

ADM formalism we introduce a family of spatial hyperslices. This allows us to think of as the geometry of "space" as evolving over "time". This is an attractive viewpoint, but in general no such family of hyperslices will be physically preferred. The Weyl hypothesis can be understood as the assumption that we should consider only cosmological models in which there "is" such a preferred slicing, namely the one given by taking the unique hyperslices orthogonal to the world lines of the fluid particles.One consequence of this hypothesis is that if it holds true, we can introduce a comoving chart such that the

metric tensor contains no terms of form**dt dx**,**dt dy**, or**dt dz**.The additional hypothesis that the world lines of the fluid particles be geodesics is equivalent to assuming that no body forces act within the fluid. In other words, the fluid has zero pressure, so that we are considering a

dust solution .**Relation to vorticity**The condition that the congruence corresponding to the fluid particles should be hypersurface orthogonal is by no means assured. A generic congruence does not possess this property, which is in fact mathematically equivalent to stipulating that the congruence of world lines should be "vorticity-free". That is, they should not be twisting about one another, or in other words, the fluid elements should not be swirling about their neighbors in the manner of the fluid particles in a stirred cup of coffee.

This coordinate system is called the system of

comoving coordinates .**ee also***

Shape of the Universe

* Comoving coordinates

*Friedmann-Lemaître-Robertson-Walker for the best known cosmological model (which does obey Weyl's hypothesis)

*Congruence (general relativity) , for the relatation between vorticity and hypersurfaces.

*Weyl curvature hypothesis , for a different cosmological hypothesis due toRoger Penrose .

*Wikimedia Foundation.
2010.*

### Look at other dictionaries:

**List of topics named after Hermann Weyl**— This is a list of topics named after Hermann Weyl, the influential German mathematician. * Weyl algebra * Weyl basis of the gamma matrices * Weyl chamber * Weyl character formula * Weyl s criterion * Weyl curvature: see Weyl tensor * Weyl… … Wikipedia**List of mathematics articles (W)**— NOTOC Wad Wadge hierarchy Wagstaff prime Wald test Wald Wolfowitz runs test Wald s equation Waldhausen category Wall Sun Sun prime Wallenius noncentral hypergeometric distribution Wallis product Wallman compactification Wallpaper group Walrasian… … Wikipedia**List of physics topics R-Z**— NOTOC A B C D E F G H I J K L M N O P Q R S T U V W X Y Z … Wikipedia**mathematics**— /math euh mat iks/, n. 1. (used with a sing. v.) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. 2. (used with a sing. or pl. v.) mathematical procedures,… … Universalium**Mathematical formulation of quantum mechanics**— Quantum mechanics Uncertainty principle … Wikipedia**Oskar Becker**— For the assailant of William I of Prussia, see Oskar Becker (assailant). Oscar Becker (5 September 1889 in Leipzig 13 November 1964 in Bonn) was a German philosopher, logician, mathematician, and historian of mathematics. Contents 1 Early life 2… … Wikipedia**Special relativity**— (SR) (also known as the special theory of relativity or STR) is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein (after considerable contributions of Hendrik Lorentz and Henri Poincaré) in the … Wikipedia**Relativity priority dispute**— Albert Einstein presented the theories of Special Relativity and General Relativity in groundbreaking publications that either contained no formal references to previous literature, or referred only to a small number of his predecessors for… … Wikipedia**Brouwer-Hilbert controversy**— A foundational controversy in twentieth century history of mathematics opposed L. E. J. Brouwer, a supporter of intuitionism, and David Hilbert, the founder of formalism.BackgroundThe background for the controversy was set with David Hilbert s… … Wikipedia**Introduction to special relativity**— In physics, special relativity is a fundamental theory about space and time, developed by Albert Einstein in 1905 [ On the Electrodynamics of Moving Bodies . (fourmilab.ch web site): [http://www.fourmilab.ch/etexts/einstein/specrel/www/… … Wikipedia