The following curve is geodesic in Schwardschild metric:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \tau \mapsto [(1-2m/r_0)^{-1/2}\tau,r_0,0,0][/tex].

The tangent vector is: [tex] [(1-2m/r_0)^{-1/2},0,0,0] [/tex], its length is 1 and its

product with killing vector [tex]\partial_t [/tex] is equal: [tex] (1-2m/r_0)^{1/2} = \textrm{const}[/tex]. So the body lays at rest in gravitational field - why it's possible??

In newtonian limit it's impossible - the body which does not rotate around a star cannot

have constant radious.

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# Strange geodesic in Schwartzschild metric

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