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searching for Coframe 14 found (20 total)

alternate case: coframe

Frame fields in general relativity (5,003 words) [view diff] exact match in snippet view article find links to article

defined on the manifold can be expressed using the frame field and its dual coframe field. Frame fields were introduced into general relativity by Albert Einstein

Gauge gravitation theory (1,155 words) [view diff] exact match in snippet view article find links to article

were considered as those of the translation gauge group, and a tetrad (coframe) field was identified with the translation part of an affine connection

Schwarzschild coordinates (4,089 words) [view diff] exact match in snippet view article find links to article

Cartan's exterior calculus method. First, we read off the line element a coframe field, σ 0 = − a ( r ) d t {\displaystyle \sigma ^{0}=-a(r)\,dt} σ 1 =

Isotropic coordinates (1,179 words) [view diff] exact match in snippet view article find links to article

Cartan's exterior calculus method. First, we read off the line element a coframe field, σ 0 = − a ( r ) d t {\displaystyle \sigma ^{0}=-a(r)\,dt} σ 1 =

Gaussian polar coordinates (365 words) [view diff] exact match in snippet view article find links to article

fluids Schwarzschild coordinates Isotropic coordinates Frame fields in general relativity for more about frame fields and coframe fields. v t e v t e

Van Stockum dust (2,067 words) [view diff] exact match in snippet view article find links to article

To prevent misunderstanding, we should emphasize that taking the dual coframe σ 0 = d t + h ( r ) r d φ , σ 1 = 1 f ( r ) d z , σ 2 = 1 f ( r ) d r

Maurer–Cartan form (1,992 words) [view diff] exact match in snippet view article find links to article

Kronecker delta. Then Ei is a Maurer–Cartan frame, and θi is a Maurer–Cartan coframe. Since Ei is left-invariant, applying the Maurer–Cartan form to it simply

Teleparallelism (2,612 words) [view diff] exact match in snippet view article find links to article

coefficients) in this global basis. Here ωk is the dual global basis (or coframe) defined by ωi(Xj) = δi j. This is what usually happens in Rn, in any affine

Poincaré disk model (4,060 words) [view diff] exact match in snippet view article find links to article

(}1-|\mathbf {x} |^{2}{\Bigr )}{\frac {\partial }{\partial x^{i}}},} with dual coframe of 1-forms θ i = 2 1 − | x | l 2 d x i . {\displaystyle \theta ^{i}={\frac

Torsion tensor (4,375 words) [view diff] exact match in snippet view article find links to article

the following manner. Let θ i {\displaystyle \theta ^{i}} be a parallel coframe along γ {\displaystyle \gamma } , and let x i {\displaystyle x^{i}} be

Polar coordinate system (6,702 words) [view diff] exact match in snippet view article find links to article

e_{\theta }={\frac {1}{r}}{\frac {\partial }{\partial \theta }},} with dual coframe e r = d r , e θ = r d θ . {\displaystyle e^{r}=dr,\quad e^{\theta }=rd\theta

Mathematics of general relativity (7,044 words) [view diff] exact match in snippet view article find links to article

metric tensor takes on a particularly convenient form. When allied with coframe fields, frame fields provide a powerful tool for analysing spacetimes and

Born coordinates (6,357 words) [view diff] exact match in snippet view article find links to article

Lorentzian manifold by a stationary timelike congruence. If we adopt the coframe θ 1 ^ = d z , θ 2 ^ = d r , θ 3 ^ = r d ϕ 1 − ω 2 r 2 {\displaystyle \theta

Rindler coordinates (7,773 words) [view diff] exact match in snippet view article find links to article

{\displaystyle c=1} and α = 1 {\displaystyle \alpha =1} , it is natural to take the coframe field d σ 0 = x d t , d σ 1 = d x , d σ 2 = d y , d σ 3 = d z {\displaystyle