Bianchi VIo Vacuum Solution Covariant NP Tetrad
Exact Solutions of Einstein's Field Equations
Description
Bianchi VIo vacuum solution covariant NP tetrad
Object definitions
Coframe
- TeX
- MathML
- Mathematica input
- Maple input
\left\{e_1\to \frac{d(x) \sqrt{t e^{2 n^2 t^2}}}{t}+\frac{d(t) e^{n^2 t^2}}{\sqrt{t}},e_2\to \frac{d(t)}{2}-\frac{d(x) e^{-n^2 t^2} \sqrt{t e^{2 n^2 t^2}}}{2 \sqrt{t}},e_3\to -\frac{\sqrt{t} d(z) e^{-n x}}{\sqrt{2}}-\frac{i \sqrt{t} d(y) e^{n x}}{\sqrt{2}},e_4\to -\frac{\sqrt{t} d(z) e^{-n x}}{\sqrt{2}}+\frac{i \sqrt{t} d(y) e^{n x}}{\sqrt{2}}\right\}
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{Subscript[e, 1] -> (E^(n^2*t^2)*d[t])/Sqrt[t] + (Sqrt[E^(2*n^2*t^2)*t]*d[x])/t, Subscript[e, 2] -> d[t]/2 - (Sqrt[E^(2*n^2*t^2)*t]*d[x])/(2*E^(n^2*t^2)*Sqrt[t]), Subscript[e, 3] -> ((-I)*E^(n*x)*Sqrt[t]*d[y])/Sqrt[2] - (Sqrt[t]*d[z])/(Sqrt[2]*E^(n*x)), Subscript[e, 4] -> (I*E^(n*x)*Sqrt[t]*d[y])/Sqrt[2] - (Sqrt[t]*d[z])/(Sqrt[2]*E^(n*x))}
[e[1] = exp(n^2*t^2)/t^(1/2)*d(t)+1/t*(exp(2*n^2*t^2)*t)^(1/2)*d(x), e[2] = 1/2*d(t)-1/2*exp(-n^2*t^2)/t^(1/2)*(exp(2*n^2*t^2)*t)^(1/2)*d(x), e[3] = -1/2*I*2^(1/2)*exp(n*x)*t^(1/2)*d(y)-1/2*2^(1/2)*exp(-n*x)*t^(1/2)*d(z), e[4] = 1/2*I*2^(1/2)*exp(n*x)*t^(1/2)*d(y)-1/2*2^(1/2)*exp(-n*x)*t^(1/2)*d(z)]
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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<mo>}</mo>
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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])]
Constants
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\{n\}
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{n}
[n]
Cite this as:
Exact Solutions of Einstein's Field Equations: Bianchi VIo Vacuum Solution Covariant NP Tetrad from Differential Geometry Library. http://digi-area.com/DifferentialGeometryLibrary/ExactSolutionsofEinsteinsFieldEquations/Bianchi-VIo-Vacuum-Solution-Covariant-NP-Tetrad.php
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