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Kaluza–Klein–Einstein Field Equations
In Kaluza–Klein theory, a speculative unification of general relativity and electromagnetism, the five-dimensional Kaluza–Klein–Einstein field equations are created by adding a hypothetical dimension to the four-dimensional Einstein field equations. They use the Kaluza–Klein–Einstein tensor, a generalization of the Einstein tensor, and can be obtained from the Kaluza–Klein–Einstein–Hilbert action, a generalization of the Einstein–Hilbert action. They also feature a phenomenon known as ''Kaluza miracle'', which is that the description of the five-dimensional vacuum perfectly falls apart in a four-dimensional Electrovacuum solution, electrovacuum, Maxwell's equations and an additional Graviscalar, radion field equation for the size of the compactified dimension: : \text\left\{\begin{array}{c} \text{D=4 electrovacuum Einstein field equations} \\ \text{Maxwell's equations} \\ \text{radion field equation} \end{array}\right. The Kaluza–Klein–Einstein field equations ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kaluza–Klein Theory
In physics, Kaluza–Klein theory (KK theory) is a classical unified field theory of gravitation and electromagnetism built around the idea of a fifth dimension beyond the common 4D of space and time and considered an important precursor to string theory. In their setup, the vacuum has the usual 3 dimensions of space and one dimension of time but with another microscopic extra spatial dimension in the shape of a tiny circle. Gunnar Nordström had an earlier, similar idea. But in that case, a fifth component was added to the electromagnetic vector potential, representing the Newtonian gravitational potential, and writing the Maxwell equations in five dimensions. The five-dimensional (5D) theory developed in three steps. The original hypothesis came from Theodor Kaluza, who sent his results to Albert Einstein in 1919 and published them in 1921. Kaluza presented a purely classical extension of general relativity to 5D, with a metric tensor of 15 components. Ten components are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |