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:
“Painting seems to be to the eye what dancing is to the limbs. When that has educated the frame to self-possession, to nimbleness, to grace, the steps of the dancing-master are better forgotten; so painting teaches me the splendor of color and the expression of form, and as I see many pictures and higher genius in the art, I see the boundless opulence of the pencil, the indifferency in which the artist stands free to choose out of the possible forms.”
—Ralph Waldo Emerson (1803–1882)
“Genius is the naturalist or geographer of the supersensible regions, and draws their map; and, by acquainting us with new fields of activity, cools our affection for the old. These are at once accepted as the reality, of which the world we have conversed with is the show.”
—Ralph Waldo Emerson (1803–1882)
“We raised a simple prayer
Before we left the spot,
That in the general mowing
That place might be forgot;
Or if not all so favored,
Obtain such grace of hours
That none should mow the grass there
While so confused with flowers.”
—Robert Frost (1874–1963)
“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)