Gutman Bespal Ko Space Covariant NP Tetrad
Exact Solutions of Einstein's Field Equations
Description
Covariant NP tetrad for Gutman Bespal ko space
References
Gutman, Sbornik Sovrem. Probl. Grav. Tbilissi, p201, (1967)
Wesson, J. Math. Phys., v19, p2283, (1978)
Lake, Gen. Rel. Grav., v15, p357, (1983)
Kramer et al. (14.67) p173
Object definitions
Coframe
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- Mathematica input
- Maple input
\left\{e_1\to r^2 d(t)-\frac{r d(r)}{\sqrt{1-k r^2}},e_2\to \frac{d(r)}{2 r \sqrt{1-k r^2}}+\frac{d(t)}{2},e_3\to -\frac{r d(\phi ) \sqrt{f(t)} \sin (\theta )}{\sqrt{2}}-\frac{i r d(\theta ) \sqrt{f(t)}}{\sqrt{2}},e_4\to -\frac{r d(\phi ) \sqrt{f(t)} \sin (\theta )}{\sqrt{2}}+\frac{i r d(\theta ) \sqrt{f(t)}}{\sqrt{2}}\right\}
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{Subscript[e, 1] -> -((r*d[r])/Sqrt[1 - k*r^2]) + r^2*d[t], Subscript[e, 2] -> d[r]/(2*r*Sqrt[1 - k*r^2]) + d[t]/2, Subscript[e, 3] -> ((-I)*r*d[\[Theta]]*Sqrt[f[t]])/Sqrt[2] - (r*d[\[Phi]]*Sqrt[f[t]]*Sin[\[Theta]])/Sqrt[2], Subscript[e, 4] -> (I*r*d[\[Theta]]*Sqrt[f[t]])/Sqrt[2] - (r*d[\[Phi]]*Sqrt[f[t]]*Sin[\[Theta]])/Sqrt[2]}
[e[1] = -r/(1-k*r^2)^(1/2)*d(r)+r^2*d(t), e[2] = 1/2/r/(1-k*r^2)^(1/2)*d(r)+1/2*d(t), e[3] = -1/2*I*2^(1/2)*r*d(theta)*f(t)^(1/2)-1/2*2^(1/2)*r*d(phi)*f(t)^(1/2)*sin(theta), e[4] = 1/2*I*2^(1/2)*r*d(theta)*f(t)^(1/2)-1/2*2^(1/2)*r*d(phi)*f(t)^(1/2)*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\}
<math>
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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])]
Constraints
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\left\{f(t)\to \frac{1}{2} G e^{2 t}+\frac{1}{2} H e^{-2 t}+\frac{1}{2}\right\}
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{f[t] -> 1/2 + (E^(2*t)*G)/2 + H/(2*E^(2*t))}
[f(t) = 1/2+1/2*exp(2*t)*G+1/2*exp(-2*t)*H]
Constants
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\{G,H,k\}
<math>
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{G, H, k}
[G, H, k]
Cite this as:
Exact Solutions of Einstein's Field Equations: Gutman Bespal Ko Space Covariant NP Tetrad from Differential Geometry Library. http://digi-area.com/DifferentialGeometryLibrary/ExactSolutionsofEinsteinsFieldEquations/Gutman-Bespal-Ko-Space-Covariant-NP-Tetrad.php
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