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Einstein's static universe is closed (i.e. has hyperspherical topology and positive spatial curvature), and contains uniform dust and a positive cosmological constant with value precisely = /, where is Newtonian gravitational constant, is the energy density of the matter in the universe and is the speed of light.
Einstein's static universe, aka the Einstein universe or the Einstein static eternal universe, is a relativistic model of the universe proposed by Albert Einstein in 1917. [ 1 ] [ 2 ] Shortly after completing the general theory of relativity , Einstein applied his new theory of gravity to the universe as a whole.
The Hubble eXtreme Deep Field (XDF) was completed in September 2012 and shows the farthest galaxies ever photographed at that time. Except for the few stars in the foreground (which are bright and easily recognizable because only they have diffraction spikes), every speck of light in the photo is an individual galaxy, some of them as old as 13.2 billion years; the observable universe is ...
A "closed universe" is necessarily a closed manifold. An "open universe" can be either a closed or open manifold. For example, in the Friedmann–Lemaître–Robertson–Walker (FLRW) model, the universe is considered to be without boundaries, in which case "compact universe" could describe a universe that is a closed manifold.
The cosmological constant was originally introduced in Einstein's 1917 paper entitled “The cosmological considerations in the General Theory of Reality”. [2] Einstein included the cosmological constant as a term in his field equations for general relativity because he was dissatisfied that otherwise his equations did not allow for a static universe: gravity would cause a universe that was ...
For example, d-wave or triplet superconductor, or a Fulde–Ferrell–Larkin–Ovchinnikov superconductor. Ferromagnetic superconductor: Materials that display intrinsic coexistence of ferromagnetism and superconductivity. Charge-4e superconductor: A proposed state in which electrons are not bound as Cooper pairs but as quadruplets of electrons.
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Thus, the Kerr solution provides an example of a stationary spacetime that is not static; the non-rotating Schwarzschild solution is an example that is static. Formally, a spacetime is static if it admits a global, non-vanishing, timelike Killing vector field which is irrotational, i.e., whose orthogonal distribution is involutive.