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binbagsss
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Homework Statement
Conserved quantity Schwarzschild metric.
Homework Equations
The Attempt at a Solution
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##\partial_u=\delta^u_i=k^u## is the KVF ##i=1,2,3##
We have that along a geodesic ##K=k^uV_u## is constant , where ##V^u ## is the tangent vector to some affinely parameterised geodesic.
For example if we take the Schwarzschild metric, ##K^u=(1,0,0,0)## , ##V^u=(\dot{t},\dot{r},\dot{\theta},\dot{\phi})## so we get ##K= (1-\frac{2GM}{r})\dot{t}## is conserved, for example.
where dot denotes a derivative with respect to some affine parameter ##s##
QUESTION:
What here is to say that ##s## is an affine parameter?
I.e- why is ##V^u=(\dot{t},\dot{r},\dot{\theta},\dot{\phi})## the tangent vector to an affinely parameterised geodesic?
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