Minkowski Space In Polar Coordinates Covariant NP Tetrad
Exact Solutions of Einstein's Field Equations
Description
Covariant NP tetrad for Minkowski space in polar coordinates
Object definitions
Coframe
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\left\{e_1\to d(r)+d(t),e_2\to \frac{d(t)}{2}-\frac{d(r)}{2},e_3\to -\frac{r d(\theta )}{\sqrt{2}}-\frac{i r d(\phi ) \sin (\theta )}{\sqrt{2}},e_4\to -\frac{r d(\theta )}{\sqrt{2}}+\frac{i r d(\phi ) \sin (\theta )}{\sqrt{2}}\right\}
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{Subscript[e, 1] -> d[r] + d[t], Subscript[e, 2] -> -d[r]/2 + d[t]/2, Subscript[e, 3] -> -((r*d[\[Theta]])/Sqrt[2]) - (I*r*d[\[Phi]]*Sin[\[Theta]])/Sqrt[2], Subscript[e, 4] -> -((r*d[\[Theta]])/Sqrt[2]) + (I*r*d[\[Phi]]*Sin[\[Theta]])/Sqrt[2]}
[e[1] = d(r)+d(t), e[2] = -1/2*d(r)+1/2*d(t), e[3] = -1/2*2^(1/2)*r*d(theta)-1/2*I*2^(1/2)*r*d(phi)*sin(theta), e[4] = -1/2*2^(1/2)*r*d(theta)+1/2*I*2^(1/2)*r*d(phi)*sin(theta)]
Metric
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\left\{g\to e_1\otimes e_2+e_2\otimes e_1-e_3\otimes e_4-e_4\otimes e_3\right\}
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{g -> Subscript[e, 1] \[CircleTimes] Subscript[e, 2] + Subscript[e, 2] \[CircleTimes] Subscript[e, 1] - Subscript[e, 3] \[CircleTimes] Subscript[e, 4] - Subscript[e, 4] \[CircleTimes] Subscript[e, 3]}
[g = `&.`(e[1],e[2])+`&.`(e[2],e[1])-`&.`(e[3],e[4])-`&.`(e[4],e[3])]
Cite this as:
Exact Solutions of Einstein's Field Equations: Minkowski Space In Polar Coordinates Covariant NP Tetrad from Differential Geometry Library. http://digi-area.com/DifferentialGeometryLibrary/ExactSolutionsofEinsteinsFieldEquations/Minkowski-Space-In-Polar-Coordinates-Covariant-NP-Tetrad.php
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