- #1

- 1,208

- 9

## Main Question or Discussion Point

## Homework Statement

Conserved quantity Schwarzschild metric.

## Homework Equations

## The Attempt at a Solution

[/B]

##\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:

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?

Last edited by a moderator: