Insights The Schwarzschild Metric: Part 2, The Photon Sphere - Comments

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Greg Bernhardt submitted a new PF Insights post

The Schwarzschild Metric: Part 2, The Photon Sphere
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and I used that metric in The Schwarzschild Metric: Part 1, GPS Satellites
is broken (it tries to take one to the edit page of the intended page)
 
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[URL='https://www.physicsforums.com/insights/author/urs-schreiber/']Urs Schreiber[/URL] said:
The link behind is broken (it tries to take one to the edit page of the intended page)
Fixed, thanks!
 
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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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