- #1
paweld
- 255
- 0
The following curve is geodesic in Schwardschild metric:
[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.
[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.