So ive been working on this problem. Im given the metric in Kruskal coordinates, so(adsbygoogle = window.adsbygoogle || []).push({});

ds^2=32M^2exp(-r/2M)/r(-dT^2+dX^2)+r^2(dθ^2+sin^2(θ)dΦ^2)

And the path of a particle is

X=0 T=λ θ=π/2 Φ=0

And the path of the observer is

X=-1/2*T+1/2 θ=π/2 Φ=0

And im asked to find the 3 velocity of the particle as seen by the observer when the two intersect. So far this is what i have

The 4-velocity of the observer in Kruskal Coordinates is

u=√[4/3*r/(32M^2exp(-r/2M)](1,-1/2,0,0)

So, I think i need to find a local intertial frame, but im unsure how to do that and im not sure what to do with it once ive found it! Thanks in advance!

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# Transformation to a local inertial Frame

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