Proof of Buchdal's Theorem | Show & Send Link

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Can anyone show me a proof of this theorem? Could someone possibly send me a link?
 
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http://prola.aps.org/abstract/PR/v116/i4/p1027_1
General Relativistic Fluid Spheres
H. A. Buchdahl
Phys. Rev. 116, 1027 - 1034 (1959)
 
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In Philippe G. Ciarlet's book 'An introduction to differential geometry', He gives the integrability conditions of the differential equations like this: $$ \partial_{i} F_{lj}=L^p_{ij} F_{lp},\,\,\,F_{ij}(x_0)=F^0_{ij}. $$ The integrability conditions for the existence of a global solution ##F_{lj}## is: $$ R^i_{jkl}\equiv\partial_k L^i_{jl}-\partial_l L^i_{jk}+L^h_{jl} L^i_{hk}-L^h_{jk} L^i_{hl}=0 $$ Then from the equation: $$\nabla_b e_a= \Gamma^c_{ab} e_c$$ Using cartesian basis ## e_I...
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