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:
“It would be nice to travel if you knew where you were going and where you would live at the end or do we ever know, do we ever live where we live, we’re always in other places, lost, like sheep.”
—Janet Frame (b. 1924)
“Within the regions of the air,
Compassed about with heavens fair,
Great tracts of land there may be found
Enriched with fields and fertile ground;
Where many numerous hosts
In those far distant coasts,
For other great and glorious ends,
Inhabit, my yet unknown friends.”
—Thomas Traherne (1636–1674)
“Each victim of suicide gives his act a personal stamp which expresses his temperament, the special conditions in which he is involved, and which, consequently, cannot be explained by the social and general causes of the phenomenon.”
—Emile Durkheim (1858–1917)
“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)