- #1

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I am given the initial data: the light ray is fired in the ##x## direction at ##t=0##.

The relvant coordinates in the question are ##t,x,y,z##, let ##s## be the affine paramater I parameterise the geodesics with.

MY QUESTION

Q1)Concerning the intial data, does this mean that at ##t=0##, ##\dot{y}=\dot{z}=0## and ##\dot(z)\neq 0 ##? where ##\dot{x}## denotes ##\frac{dx}{ds}## .

Q2)And not ##\frac{dy}{dt}=\frac{dz}{dt}=0##? can we only make conclusions on the change with respect ##s##, or is it with respect to the coordinate time ##t## too?

Q3)Also, is one always free to choose initially that ##s=t=0##. If so, then if the answer to question 1 is yes, doesn't this imply the answer to question 2 is yes?

Many thanks