Ornstien-Zernike equation with the assumption of spherical symmetry . ? is the liquid density, r is the separating distance, h ( r ) is the total correlation function, c ( r ) is the direct correlation function.
42.
A vector field has spherical symmetry if it is in radially inward or outward direction with a magnitude and orientation ( inward / outward ) depending on the distance to the origin only, such as a central force.
43.
On each hypersurface of constant t, constant \ theta and constant \ phi ( i . e ., on each radial line ), g _ { 11 } should only depend on r ( by spherical symmetry ).
44.
The first module, or fission trigger, exploded by compression of nuclear material or fission and fusion of materials by spherical explosion of chemical explosives, in which the spherical symmetry of the implosion was dictated by the initial spherically symmetric detonation of the explosive .
45.
In particular, the three spatial Killing vector fields have exactly the same form as the three nontranslational Killing vector fields in a spherically symmetric chart on E 3; that is, they exhibit the notion of arbitrary Euclidean rotation about the origin or spherical symmetry.
46.
But that ought to be impossible; because the gravitational fields of a hollow sphere and a solid one of the same mass are identical, it would seem that such an experiment could only detect departures from spherical symmetry, not the distribution of mass by depth.
47.
Due to the observation that larger voids predominantly remain in a linear regime, with most structures within exhibiting spherical symmetry in the underdense environment; that is, the underdensity leads to near-negligible particle-particle gravitational interactions that would otherwise occur in a region of normal galactic density.
48.
The intuitive idea of Birkhoff's theorem is that a spherically symmetric gravitational field should be produced by some massive object at the origin; if there were another concentration of mass-energy somewhere else, this would disturb the spherical symmetry, so we can expect the solution to represent an " isolated " object.
49.
Spiral Wave referred to rotation not because of centrifugal force on " you " ( which would only matter if " you " rotated inside the star ), but because it would cause the star to become oblate, and thereby break the perfect spherical symmetry assumed by the theorem .-- talk ) 22 : 49, 22 February 2007 ( UTC)
50.
Choosing one of these hypersurfaces ( the one with radius r _ { 0 }, say ), the metric components restricted to this hypersurface ( which we denote by \ tilde { g } _ { 22 } and \ tilde { g } _ { 33 } ) should be unchanged under rotations through \ theta and \ phi ( again, by spherical symmetry ).
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