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:
“In this choice of inheritance we have given to our frame of polity the image of a relation in blood; binding up the constitution of our country with our dearest domestic ties; adopting our fundamental laws into the bosom of our family affections; keeping inseparable and cherishing with the warmth of all their combined and mutually reflected charities, our state, our hearths, our sepulchres, and our altars.”
—Edmund Burke (1729–1797)
“Like a man traveling in foggy weather, those at some distance before him on the road he sees wrapped up in the fog, as well as those behind him, and also the people in the fields on each side, but near him all appears clear, though in truth he is as much in the fog as any of them.”
—Benjamin Franklin (1706–1790)
“The General Order is always to manoeuver in a body and on the attack; to maintain strict but not pettifogging discipline; to keep the troops constantly at the ready; to employ the utmost vigilance on sentry go; to use the bayonet on every possible occasion; and to follow up the enemy remorselessly until he is utterly destroyed.”
—Lazare Carnot (1753–1823)
“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)