Frame Fields In General Relativity
In general relativity, a frame field (also called a tetrad or vierbein) is a set of four orthonormal vector fields, one timelike and three spacelike, defined on a Lorentzian manifold that is physically interpreted as a model of spacetime. The timelike unit vector field is often denoted by and the three spacelike unit vector fields by . All tensorial quantities defined on the manifold can be expressed using the frame field and its dual coframe field.
Frames were introduced into general relativity by Hermann Weyl in 1929.
The general theory of tetrads (and analogs in dimensions other than 4) is described in the article on Cartan formalism; the index notation for tetrads is explained in tetrad (index notation).
Read more about Frame Fields In General Relativity: Physical Interpretation, Specifying A Frame, Specifying The Metric Using A Coframe, Relationship With Metric Tensor, in A Coordinate Basis, Comparison With Coordinate Basis, Nonspinning and Inertial Frames, Example: Static Observers in Schwarzschild Vacuum, Example: Lemaître Observers in The Schwarzschild Vacuum, Example: Hagihara Observers in The Schwarzschild Vacuum, Generalizations
Famous quotes containing the words frame, fields, general and/or relativity:
“We are not permitted to choose the frame of our destiny. But what we put into it is ours.”
—Dag Hammarskjöld (1905–1961)
“As the fields fear drought in autumn, so people fear poverty in old age.”
—Chinese proverb.
“Every writer is necessarily a critic—that is, each sentence is a skeleton accompanied by enormous activity of rejection; and each selection is governed by general principles concerning truth, force, beauty, and so on.... The critic that is in every fabulist is like the iceberg—nine-tenths of him is under water.”
—Thornton Wilder (1897–1975)
“By an application of the theory of relativity to the taste of readers, to-day in Germany I am called a German man of science, and in England I am represented as a Swiss Jew. If I come to be regarded as a bête noire the descriptions will be reversed, and I shall become a Swiss Jew for the Germans and a German man of science for the English!”
—Albert Einstein (1879–1955)